We show that the solid-solution series LixCryCo1-yO2 can be prepared as a single phase with x near 1 for 0 less-than-or-equal-to y less-than-or-equal-to 0.5 and y = 1.0. Using powder X-ray diffraction and Rietveld profile refinement, we show that these solid-solutions are isostructural with LiCoO2 but with Cr and Co sharing the Co sites. Electrochemical measurements using Li/LixCryCo1-yO2 cells show that as y increases the amount of Li which can be reversibly cycled in these materials decreases drastically, thus limiting the practical usefulness of these materials. We were unsuccessful at making single-phase solid-solutions of LixCrNi1-yO2 using similar methods.