We present results from a study of ab-type RR Lyrae variables in the Large Magellanic Cloud (LMC) using the extensive data set from phase III of the Optical Gravitational Lensing Experiment (OGLE; Udalski et al.). The metallicities of the RR Lyraes, determined from the periods and amplitudes of their light curves, reveal a statistically significant radial abundance gradient that is approximately one-half of what is seen in the discs of the Milky Way and M33. The RR Lyrae abundance gradient agrees with that of the old and metal-poor LMC globular clusters. The reddenings of the OGLE RR Lyraes have been calculated using their minimum light colours and reveal a mean value of E(V - I) = 0.12±0.05, where the quoted uncertainty represents the standard deviation of the mean. The distribution of RR Lyrae extinctions across the face of the LMC is well correlated with the distribution and emission intensity of CO clouds based on recent millimetre wave surveys. In addition, we find that the old LMC globulars tend to be located in regions of low extinction. This underscores the need to survey the higher extinction regions with the specific aim of increasing the sample of old LMC globular clusters. Finally, we examine the distance distribution of the RR Lyraes in order to probe the structure of the LMC and investigate the possibility that some of the RR Lyraes may reside in a kinematically hot halo population. In addition to calculating a mean LMC distance of (m - M)o = 18.55±0.10mag, we conclude that some fraction of the RR Lyraes in our sample could be members of the LMC halo.