This will be a double-blind (patient and study staff will not know the identity of assigned treatment), randomized (assignment to 1 to 3 treatment groups will be by chance, like "flipping a coin"), placebo-controlled, multiple dose study conducted at up to two clinical sites. Up to 42 patients with osteoarthritis of the knee will be enrolled in 3 cohorts (Cohort 1 to 3). Additional cohorts (up to 14 patients per cohort) may be added after completion of Cohort 3. The study consists of eligibility screening, a treatment phase, and 4 follow-up visits. The study duration for each patient will be approximately 10 weeks. Patients safety will be closely monitored during the study by review of adverse events, electrocardiograms, vital signs (including oral temperature), clinical laboratory tests, and physical examinations. During specified study visits, blood samples will be collected for pharmacokinetics, pharmacodynamics (inpatient patients), and pharmacogenomic (optional) evaluations of JNJ-39439335. The effectiveness of JNJ-39439335 will be evaluated by assessing pain using an 11-point numerical rating scale and by the Western Ontario and McMaster Osteoarthritis Index. In Cohort 1 and 2, all patients will take their study medication orally, twice a day for 21 days. The treatment groups for Cohort 1 are JNJ-39439335 10 mg, naproxen 500 mg every 12 hours, and placebo. The treatment groups for Cohort 2 are JNJ-39439335 25 mg, naproxen 500 mg every 12 hours, and placebo. The treatment groups for Cohort 3 will be determined based on the results of Cohort 1 and 2.