This phase II trial compares the effect of initial vaccination (PCV20 followed by PSV23) with yearly vaccinations of PSV23 to the standard 5 year vaccination in patients with chronic lymphocytic leukemia. At present chronic lymphocytic leukemia patients are poorly protected by anti-pneumococcal vaccination. Current vaccination schedule for chronic lymphocytic leukemia patients is based on general recommendations in immunocompromised patients (initial vaccination with PCV13 followed by one dose of PSV23 after an interval of two months, followed by revaccination at 5 years). Giving patients frequent immunization as compared to 5 year immunization may result in higher protective titers in patients.

PRIMARY OBJECTIVE:

I. Proportion of patients with anti-pneumococcal immunogenicity following early revaccination (1 year) at 2 years (Serotype to be measured are 1, 3, 4, 5, 6A, 6B, 7F, 9V, 14, 18C, 19A 19 F and 23F using the enzyme-linked immunosorbent assay [ELISA] method).

SECONDARY OBJECTIVES:

I. Number of patients with anti-pneumococcal immunogenicity at 5 years. II. Number of patients with local and/or general reaction at months 1, 3 as self-reported.

III. Number of pneumococcal infections.

OUTLINE: Patients are randomized to 1 of 2 arms.

ARM A: Patients receive PCV 20 IM at week 0. Titers will be checked 4 weeks after this dose. Booster Vaccine: None. Titers will be checked at 12 weeks and then yearly for 5 years.

ARM B: Patients receive PCV 20 IM at week 0 and PSV23 IM at week 8. Titers will be checked 4 weeks after the first dose and at 12 weeks (4 weeks after the second dose). Booster Vaccine: None. Annual titers will be checked for 5 years.

ARM C: Patients receive PCV 20 IM at week 0 and PSV23 IM at week 8. Titers will be checked 4 weeks after the first dose and at 12 weeks (4 weeks after the second dose). Booster Vaccine: PCV23 booster vaccination dose will be administered yearly for 5 years. Pre-vaccination and post-vaccination (at 4 weeks) titers will be checked each time yearly for 5 years.

Inclusion Criteria:

• Men and women >= 18 years of age
• Patients must have histologically identified chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) as defined by the World Health Organization (WHO) classification of hematopoietic neoplasms
• Treatment naive CLL/SLL; No prior therapy for CLL/SLL, including chemotherapy and/or radiotherapy is allowed
• Estimated life expectancy of greater than 24 months

Exclusion Criteria:

• Patients with neutropenic (granulocyte [PMN]s < 500 cells/mm^3) or having received rituximab within 6 months
• Patients with fever (temperature > 38 degrees Celsius [C]) within 1 week
• Active infection, recent infection requiring systemic treatment that was completed =< 14 days before starting treatment on the study
• Patients with known human immunodeficiency virus (HIV) infection
• History of allergic reactions attributable to compounds of similar chemical or biologic composition to any component of pneumococcal vaccines
• Chemotherapy in 4 weeks or received Rituximab or similar anti CD20 monoclonal antibody for non-hematological indications within 6 months
• Received intravenous immunoglobulin (IVIG) within 3 months prior to vaccination
• History of allogenic stem cell transplantation
• Patients who have received cellular therapy (e.g. CAR-T cells) within 12 months prior to vaccination
• Patients who have previously received pneumococcal vaccine within the preceding 12 months
• Absolute lymphocyte count less than 500 cells/mm^3
• Patient with other severe immune deficiency
• Patients may not be receiving any other investigational agents
• Active malignancy from which the subject is considered by his or her physician to have a less than 24 month survival expectation. Non-melanoma skin cancer is not an exclusion criterion.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection and/or psychiatric illness/social situations that would limit compliance with study requirements
• Concurrent systemic immunosuppressant therapy (e.g., cyclosporine A, tacrolimus, etc., or chronic administration [> 14 days] of > 20 mg/day of prednisone) within 14 days of the first dose of study drug
• Because of the potential for H2-blockers to modulate antibody response to pneumococcal vaccine, patients must discontinue treatment with H2-blockers (cimetidine, ranitidine, etc.) prior to beginning protocol therapy
• Unwilling or unable to participate in all required study evaluations and procedures
• Unable to understand the purpose and risks of the study and to provide a signed and dated informed consent form (ICF) and authorization to use protected health information (in accordance with national and local subject privacy regulations)