In this study, both relative rate and absolute kinetic measurements were made at 298 K for the reaction of chlorine atoms with the C1-C4 alkanes. The relative rate studies were carried out using two different reaction chambers and GC to follow the loss of the organics upon reaction with atomic chlorine generated from the photolysis of Cl-2 or CINO. Relative rate studies were also carried out for the chloro-substituted methanes. Absolute rate constant studies employed a fast flow discharge system with resonance fluorescence detection of atomic chlorine. Our relative rate constants for the ethane/propane and ethane/n-butane pairs are approximately 15 and 20% lower respectively than recent measurements carried out on a similar series of alkanes. The absolute rate constant for propane is 20% lower than previous absolute rate measurements and the currently recommended value. However, the ratios of the absolute rate constants measured in this study agree to within 10% with our independently measured relative rate constants. Thus, these studies provide for the first time a consistent set of reaction rate constants for the reaction of Cl with the simple alkanes. While the rate constants derived for CH3Cl and CH2Cl2 are in reasonably good agreement with the literature, that for CHCl3 is approximately 50% higher (but within the wide error bars) of current recommendations. The trends in the rate constants are discussed in the context of recently derived structure-activity relationships.