Neutrophils are thought to play an important role in the pathophysiology of chronic obstructive pulmonary disease (COPD). Navarixin (SCH 527123, MK-7123) is an antagonist of the cysteine-X-cysteine chemokine receptor 2 (CXCR2) and is thought to reduce neutrophil migration to the diseased lung. It is theorized that reducing neutrophil migration to the diseased lung will improve a participant's symptoms and the natural history of the disease. The study will consist of a 2-week screening period followed by a 2-year (104-week) double-blind treatment period. The 2-year Treatment Period will be made up of two phases: a 26-week (6-month) dose range-finding phase with 3 active arms and 1 placebo arm (Period 1), followed by a 78-week (18-month) long-term safety and efficacy phase (Period 2). Participants participating in the original 6-month study (Period 1) may elect not to continue into the 18-month extension study (Period 2). Hypothesis: navarixin, 50 mg, or the highest remaining dose if the 50-mg dose is discontinued, is superior to placebo with respect to improving airflow.