 This multicenter, double-blind, randomized, placebo-controlled study will evaluate the safety of a single infusion of tocilizumab versus placebo, administered in addition to standard premedications antipyretic, antihistamine, and corticosteroid prior to the first infusion of obinutuzumab administered in combination with oral chlorambucil to participants with previously untreated B-CLL who have comorbidities. All eligible participants will be treated with a total of 6 cycles of obinutuzumab chlorambucil cycle length 28 days. 