This is an open-label (individuals will know the identity of study treatments), dose escalation study to establish the recommended dose of ibrutinib combined with standard R-CHOP (rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone) in approximately 33 adults with CD20-positive B-cell non-Hodgkin lymphoma (NHL) for whom R-CHOP is an appropriate therapy. There will be 3 periods of the study: a pretreatment (screening) period of up to 28 days before enrollment; an open-label treatment period (up to 6 cycles of ibrutinib and R-CHOP; ending at the end-of-treatment visit); and a posttreatment follow-up period until the end of study (maximum of up to 1 year after the last patient has completed the end-of-treatment visit). There are 2 parts to the study (dose escalation [Part 1] and expansion [Part 2]). During the dose escalation period, the "3+3" design will be applied and approximately 18 patients with CD20 positive B cell NHL (diffuse large B-cell lymphoma [DLBCL], mantle cell lymphoma [MCL], and follicular lymphoma [FL]) may be enrolled. Patients will be assigned to cohorts of increasing oral daily doses of ibrutinib (280, 420, and 560 mg) administered in combination with R-CHOP. The maximum tolerated dose (MTD), assessed in Cycle 1 (dose-limiting toxicity [DLT] period), is defined as the highest dose of the combination regimen at which <=33% of patients experience DLT. Baseline and follow-up electrocardiograms will be performed throughout the study. A Study Evaluation Team will review all available data upon completion of the first cycle for all patients at each dose cohort to determine DLTs, if dose escalation is acceptable, and subsequently will determine the recommended Phase 2 dose. Once the recommended Phase 2 dose is determined, approximately 15 patients with newly diagnosed DLBCL will be entered into the expansion cohort at the dose level selected to further assess the safety, pharmacokinetics, pharmacodynamics, pharmacogenomics, and activity of the combination. Patients whose disease has not progressed at the end of Cycle 1 will continue to receive ibrutinib and R CHOP up to a maximum of 6 cycles. During the posttreatment follow-up period, long term safety, survival status, disease progression, and subsequent antilymphoma therapy will be collected. The study will end 1 year after the last patient has completed the end of treatment visit.