We describe a series of measurements of pressure-broadening coefficients for the F' = 3 <-- F" = 4 line of the P-2(1/2) <--2P(3/2) transition in atomic iodine. This is the optical transition of the chemically pumped atomic iodine laser (COIL), and our results are relevant to a more complete understanding of this important class of high-power lasers. The measurements were made in sealed cells using an argon ion laser to photodissociate molecular iodine and a tunable diode laser to probe directly the atomic transition. We measured broadening coefficients for three bath gases: He, N-2, and O-2: Full absorption line shapes were recorded as a function of the added bath gas pressure and the following values were obtained at room temperature: (Deltanu/DeltaP(He))(T=296K) = 3.2 +/- 0.3 MHz/Torr, (Deltanu/DeltaP(N2))(T=296K) = 5.5 +/- 0.6 MHz/Torr, and (Deltanu/DeltaP(O2))(T=296K) = 5.0 +/- 0:5 MHz/Torr; where Deltanu is the full width at half-maximum. We also measured the temperature dependencies of the He and O-2 broadening coefficients over the range 296 K < T < 775 K. We quote the temperature-dependent values as (Deltanu/DeltaP(He))(T) = (3.2 +/- 0.3) x (296/7)(0.36) and (Deltanu/DeltaP(O2))(T) = (5.5 +/-0.6) x (296/T)(0.70). Comparisons to previous measurements are also discussed.