Inclusion Criteria:

          -  Diagnosis of B-CLL, confirmed by flow cytometry and as per the criteria outlined by
             the IWCLL/Hallek December 2008

          -  Patients must have relapse or refractory CLL/SLL who have received at least 1 prior
             anti-CLL/small lymphocytic lymphoma (SLL) therapy. (Note: There is no upper limit of
             how many lines of therapy the patient may have received previously)

               -  Note: For the purpose of a particular therapy/regimen to be counted towards the
                  number of prior treatments a patient must have received at least 2 cycles of the
                  regimen e.g., a patient who change their treatment regimen after only 1 cycle
                  (due to toxicity or any other reason) will not be considered to have "2" prior
                  therapies

          -  Cohort 1 only: Exposed to ibrutinib. Patients must meet one of the following criteria:

               -  They have been previously treated with ibrutinib and were taken off for any
                  reason (except grade 4 toxicity definitely attributed to ibrutinib) as long as
                  deemed safe by the treatment physician to receive ibrutinib again

               -  Currently on ibrutinib and now have progressive disease (ibrutinib refractory)

               -  Currently on ibrutinib and have failed to achieve either a complete remission
                  after at least 12 cycles of treatment with ibrutinib or have suboptimal response
                  (< partial response [PR]) after being on ibrutinib treatment for 6 cycles

          -  Patients must have a measurable disease

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 at
             registration

          -  Absolute neutrophil count >= 1000/mm^3 (obtained =< 14 days prior to registration)

          -  Platelets >= 50,000/mm^3 (obtained =< 14 days prior to registration)

          -  Serum creatinine =< 1.5 x upper limit of normal (ULN) (minimal acceptable creatinine
             clearance [CLcr] > 25 ml/min) (obtained =< 14 days prior to registration)

          -  Total bilirubin =< 1.5 mg/dL or direct bilirubin =< 1.0 mg/dL for patients with
             Gilbert's syndrome (obtained =< 14 days prior to registration)

          -  Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase [AST]) and
             serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) =< 3 x
             ULN (obtained =< 14 days prior to registration)

          -  Women of childbearing potential and men who are sexually active must be practicing a
             highly effective method of birth control during and after the study consistent with
             local regulations regarding the use of birth control methods for subjects
             participating in clinical trials. Men must agree to not donate sperm during and after
             the study. For females, these restrictions apply for 3 months after the last dose of
             study drug. For males, these restrictions apply for 3 months after the last dose of
             study drug

          -  Negative pregnancy test done =< 14 days prior to registration, for persons of
             childbearing potential only

               -  NOTE: If the urine test is positive or cannot be confirmed as negative, a serum
                  pregnancy test will be required

          -  Provide written informed consent

          -  Willing to return to enrolling institution for follow-up (during the Active Monitoring
             Phase of the study)

        Exclusion Criteria:

          -  Any serious medical condition, laboratory abnormality, or psychiatric illness that
             would prevent the subject from signing the informed consent form

          -  Patient is known to have chronic obstructive pulmonary disease with a forced
             expiratory volume in 1 second (FEV1) < 50% of predicted normal (Note: FEV1 testing is
             required for subjects suspected of having chronic obstructive pulmonary disease and
             subjects must be excluded if FEV1 < 50% of predicted normal)

          -  Patient is known to have moderate or severe persistent asthma within the past 2 years,
             or currently has uncontrolled asthma of any classification (Note: subjects who
             currently have controlled intermittent asthma or controlled mild persistent asthma are
             allowed in the study)

          -  Since this study involves an investigational agent whose genotoxic, mutagenic and
             teratogenic effects on the developing fetus and newborn are unknown, any of the
             following will deem the subject ineligible for the study:

               -  Pregnant women

               -  Nursing women

               -  Men or women of childbearing potential who are unwilling to employ adequate
                  contraception

          -  Any condition, including the presence of laboratory abnormalities, which places the
             subject at unacceptable risk if he/she were to participate in the study or confounds
             the ability to interpret data from the study

          -  Use of any other experimental drug or therapy =< 14 days prior to registration on this
             study

               -  NOTE: Patients on low dose prednisone (=< 10 mg) for treatment of conditions
                  other than CLL are eligible

          -  Patients who have received no prior therapy for CLL

          -  Patients with history of any other cancer (except non-melanoma skin cancer or
             carcinoma in-situ of the cervix, unless in complete remission and off therapy for that
             disease for > 3 years)

          -  Patients who have previously received daratumumab on a clinical trial or for any other
             malignancy

          -  Concomitant use of warfarin or other vitamin K antagonists

          -  Requires treatment with a strong cytochrome P450 modulators (CYP3A inhibitor and/or
             CYP3A inducers)

          -  Major surgery =< 4 weeks prior to registration

          -  Patients who are:

               -  Seropositive for human immunodeficiency virus (HIV)

               -  Seropositive for hepatitis B (defined by a positive test for hepatitis B surface
                  antigen [HBsAg]). Subjects with resolved infection (i.e., subjects who are HBsAg
                  negative but positive for antibodies to hepatitis B core antigen [anti-HBc]
                  and/or antibodies to hepatitis B surface antigen [anti-HBs]) must be screened
                  using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus
                  (HBV) deoxyribonucleic acid (DNA) levels. Those who are PCR positive will be
                  excluded. EXCEPTION: Subjects with serologic findings suggestive of HBV
                  vaccination (anti-HBs positivity as the only serologic marker) AND a known
                  history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR

               -  Seropositive for hepatitis C (except in the setting of a sustained virologic
                  response [SVR], defined as aviremia at least 12 weeks after completion of
                  antiviral therapy)