We present an analysis of Chandra High Energy Transmission Grating (HETG) spectra of the corona of the critical intermediate-activity, quadruple stellar system ξ UMa. Using the maximum A/B subsystem separation in 2001, we attempted to resolve for the first time in X-rays the two components using the HETG Medium Energy Grating (MEG). We found the Aa component of the system to be at least 2 orders of magnitude fainter than the Bb component. We used the Markov Chain Monte Carlo method to reconstruct differential emission measures (DEMs) and abundances and discuss first ionization potential (FIP) issues. The reconstructed DEMs showed two pronounced peaks at logT~6.5 and logT~7.0 K, respectively, similar to brighter solar active regions. A plot of coronal abundances, with respect to stellar photospheric, versus FIP reveals that the FIP behavior of ξ UMa is intermediate between less and more active stars, commensurate with its X-ray luminosity. The abundances of Mg, Fe, and Si are just subsolar, with Fe having the lowest abundance of these. The low-FIP elements Na and Al have similar abundances, and they are both higher than the Mg, Fe, and Si group. The abundances show a minimum at S, rising gradually to Ne, which is higher than photospheric, as has been seen by other authors on similar stars. Some of the FIP behavior seen here is predicted by the new ponderomotive force model of Laming.