We present the first spatially separated X-ray observation of the active UV Ceti binary with \textit{Chandra}, providing important new information on the relative X-ray activity levels of its nearly identical dM5.5e components. The two components had similar X-ray luminosities during low-level periods and emission measure loci derived from Low Energy Transmission Grating spectra reveal similar coronal temperatures ($3 - 6$ MK). However, the B component showed a higher degree of variability, resulting in a higher average X-ray luminosity than that of UV Cet A. We discuss possible causes of this enhanced activity in UV Ceti B.