This paper presents an application of the reaction class transition state theory (RC-TST) to predict thermal rate constants for hydrogen abstraction reactions of the type OH + alkane -> HOH + alkyl. We have derived all parameters for the RC-TST method for this reaction class from rate constants of 19 representative reactions, coupling with linear energy relationships (LERs), so that rate constants for any reaction in this class can be predicted from its reaction energy calculated at either the AM I semiempirical or BH&HLYP/cc-pVDZ level of theory. The RC-TST/LER thermal rate constants for selected reactions are in good agreement with those available in the literature. Detailed analyses of the results show that the RC-TST/LER method is an efficient method for accurately estimating rate constants for a large number of reactions in this class. Analysis of the LERs leads to the discovery of the P-carbon radical stabilization effect that stabilizes the transition state of any reaction in this class that yields products having one or more P-carbons. and thus leads to the lower barrier for such a reaction.