The rate constant of the gas-phase addition reaction of the light hydrogen isotope muonium to molecular oxygen, Mn + O-2 --> MuO(2), was measured over a range of temperatures from 115 to 463 K at a pressure of 2 bar and from 16 to 301 bar at room temperature, using N-2 as the moderator gas. The reaction remains in the termolecular regime over the entire pressure range. At room temperature, the average low-pressure limiting rate constant is k(ch)(0)(Mu) = (8.0 +/- 2.1) x 10(-33) cm(6) s(-1), a factor of almost 7 below the corresponding rate constant for the H + O-2 addition reaction, k(ch)(0)(H). In contrast to k(ch)(0)(H), which exhibits a clear negative temperature dependence, k(ch)(0)(MU) is essentially temperature independent. At room temperature, the kinetic isotope effect (KIE) is strongly pressure (density) dependent and is reversed at pressures near 300 bar. The kinetics are analyzed based on the statistical adiabatic channel model of Tree using a Morse potential, which works well in reproducing the overall KIE. The major factors governing the isotope effect are differences in the moment of inertia and density of vibrational states of the addition complex.