Recent evidence has shown that the mesospheric sodium nightglow, a chemiluminescent process which produces atomic sodium D-line radiation in the Earth's upper atmosphere, proceeds through the first excited (A (2)Sigma (+)) electronic state of NaO. The rate of D-line radiation production is proportional to the rate constant for the reaction of NaO(A (2)Sigma (+)) + O(P-3) and its branching ratio to produce excited Na(P-2) rather than ground-state Na(S-2). The only previously published measurement of the NaO + O(P-3) reaction rate and branching ratio was performed under slow flow conditions and almost certainly primarily represents the reaction of ground state NaO (X (2)Pi). We present low-pressure measurements of the NaO + O reaction kinetics using an NaO source reaction known to produce NaO in the (A (2)Sigma (+)) state and determine the 290 K reaction rate constant to be (5.1 +/- 1.8) x 10(-10) cm(3) s(-1) and the branching ratio to produce Na(P-2) to be 0.14 +/- 0.04. New data on the termolecular rate coefficient for the reaction Na + O-2 + He --> NaO2 + He at 290 K are also presented.