Ruxolitinib Phosphate in Treating Patients With Previously Untreated Chronic Lymphocytic Leukemia/Small Lymphocytic Lymphoma

Inclusion: 1. Subjects who are able to understand and sign an informed consent document. 2. Subjects 18 years of age or older. 3. Subjects must be diagnosed with CLL/SLL and do not meet the IWCLL criteria for treatment 4. Patients should be previously untreated or have only been treated with single agent ibrutinib therapy for a period of \< 3 months and were deemed ibrutinib intolerant. 5. Patients whose expected time to CLL/SLL treatment, according to our nomogram posted on the leukemia protocol priority list, is four years of less. 6. Subjects with hemoglobin values at the screening visit equal to or greater than 12.0 g/dL. 7. Subjects with a platelet count of at least 100 x10\^9 at the screening visit. 8. Subjects with an absolute neutrophil count (ANC) of equal to or higher than 0.5 x10\^9 at the screening visit. 9. Subject who are willing to undergo a bone marrow aspiration and biopsy and CT scan for disease burden assessment. 10. Patient who are capable to return to MD Anderson Cancer Center (MDACC) for follow-up 11. Subjects with an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 12. Patient must be capable of swallowing the Ruxolotinib capsules (tablets). Exclusion: 1. Females who are pregnant or are currently breastfeeding. 2. Subjects of childbearing potential who are unwilling to take appropriate precautions (throughout the study from screening including 30 days after discontinuation of the study drug) to avoid becoming pregnant or fathering a child. A) Females of non-childbearing potential are defined as women who (a) are equal to or greater than 55 years of age with history of amenorrhea for 1 year, OR (b) are surgically sterile for at least 3 months. B) For females of childbearing potential, or for males, appropriate precautions are those that are at least 99% effective in preventing the occurrence of pregnancy. These methods should be communicated to the subjects and their understanding confirmed: a) Double barrier methods; b) Condom with spermicide in conjunction with use of an intrauterine device (IUD); c) Condom with spermicide in conjunction with use of a diaphragm; d) Oral, injectable, or implanted contraceptives; e) Tubal ligation or vasectomy (surgical sterilization) 3. Subjects with recent history of inadequate bone marrow reserve as demonstrated by previous transfusions except for acute blood loss (e.g. surgery) in the month prior to screening. 4. Subjects with inadequate liver or renal function at screening and baseline visits: A) Alanine aminotransferase (ALT) \> 2.5x Upper limit of normal (ULN). B) Modification of Diet in Renal Disease (MDRD) calculated GFR \< 30 mL/min 5. Subjects with active uncontrolled infection or who are HIV positive (Subjects with acute infections requiring treatment should delay screening/enrollment until the course of therapy has been completed and the event is considered controlled). 6. Subjects with a history of or a current malignancy except for treated basal or squamous carcinomas of the skin completely resected. 7. Subjects with clinically significant uncontrolled cardiac disease. 8. Subjects being treated concurrently with any prohibited medications, including investigational medication, rifampin, St. John's wort, and potent CYP3A4 inhibitors (excluding ketoconazole) unless continuation of such medications are determined by the investigator to be in the best interest of the patient. Refer to protocol section 2.2.12 for more details. 9. Subjects who have previously received JAK inhibitor therapy 10. Subjects with active alcohol or drug addiction that would interfere with their ability to comply with the study requirements. 11. Subjects with any concurrent condition that, in the Investigator's opinion, would jeopardize the safety of the subject or compliance with the protocol. 12. Subjects who have unknown transfusion history. 13. Patients who cannot comply with the study requirements.