We describe a new molecular beam-luminescence method for measuring state-resolved cross sections for the quenching of metastable noble gas atoms, and report values for "dark" collisions of Ng*(P-3(2),P-3(0)) With O-2(X (3) Sigma(g)(-)), where Ng=Ar, Kr, and Xe. Cross sections for quenching sigma(Q) and, in some cases, cross sections for excited products sigma* are also given for a number of state-specific, luminescent monitor reactions. The elastic reaction of Ng* with He or Ne is employed to correct the total disappearance cross section Q(T) for viewing losses caused by nonquenching processes. The velocity-averaged, quenching cross section Q(Q) is obtained by subtracting the nonquenching cross section Q(N) from Q(T). values of Q(Q) measured at average relative velocity (g) over bar (average relative kinetic energy (E) over bar) are deconvoluted to yield sigma(Q)((g) over bar) For Ar* collisions with O-2, We find a sigma(Q)[P-3(2)] values of 35.6+/-1.8 Angstrom(2) for (g) over bar(E) between 690 and 2000 m/s (50 and 350 meV) that gradually decrease above 2000 m/s, and sigma(Q)[P-3(0)] values of 46+/-4 Angstrom(2) between 690 and 830 m/s (50 and 70 meV). For Kr* collisions, we report sigma(Q)[P-3(2)] values of 38.1+/-2.5 Angstrom(2) between 575 and 810 m/s (46 and 87 mev) with no apparent velocity dependence, and a sigma(Q)[P-3(0)] value of 56+/-7 Angstrom(2) at 576 m/s (46 meV). For Xe* collisions, we find a [P-3(2)] values of 48+/-3 Angstrom(2) at 535 m/s (44 meV) and 38+/-2 Angstrom(2) at 697 m/s (73 meV), and a sigma(Q)[P-3(0)] value of similar to 125 Angstrom(2) at 535 m/s (44 meV). Comparisons with sigma(Q) values obtained with other techniques that do not require a viewing loss correction are excellent. We also use the Ionic-Intermediate-Curve-Crossing Model (IICCM) to calculate cross sections for the Ar*(P-3(2))+O-2-->Ar+O*(D-1)+O(P-3) reaction. In our application of the model, the product state dissociative continuum is coupled to Ar+O2- through the predissociating O-2*(E (3) Sigma(u)(-)) State that is valence Rydberg in character. Values of sigma(Q) derived from the model are in good agreement with our experiment.