Phase II Comparative Study of Anti-Pneumococcal Vaccine Strategy in Patients With Chronic Lymphocytic Leukemia

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)