The reaction of the H-center dot atom with O-2, giving the hydroperoxyl HO2 center dot radical, has been investigated in pressurized water up to 350 degrees C using pulse radiolysis and deep-UV transient absorption spectroscopy. The reaction rate behavior is highly non-Arrhenius, with near diffusion-limited behavior at room temperature, increasing to a near constant limiting value of similar to 5 x 10(10) M-1 s(-1) above 250 degrees C. The high-temperature rate constant is in near-perfect agreement with experimental extrapolations and ab initio calculations of the gas-phase high-pressure limiting rate. As part of the study, reaction of the OH center dot radical with H-2 has been reevaluated at 350 degrees C, giving a rate constant of (6.0 +/- 0.5) x 10(8) M-1 s(-1). The mechanism of the H-center dot atom reaction with the HO2 center dot radical is also investigated and discussed.