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Since AlN has emerged as an important piezoelectric material for a wide variety of applications, efforts have been made to increase its piezoelectric response via alloying with transition metals that can substitute for Al in the wurtzite lattice. We report on density functional theory calculations of structure and properties of the CrxAl1-xN system for Cr concentrations ranging from zero to beyond the wurtzite-rocksalt transition point. By studying the different contributions to the longitudinal piezoelectric coefficient, we propose that the physical origin of the enhanced piezoelectricity in CrxAl1-xN alloys is the increase of the internal parameter u of the wurtzite structure upon substitution of Al with the larger Cr ions. Among a set of wurtzite-structured materials, we find that CrxAl1-xN has the most sensitive piezoelectric coefficient with respect to alloying concentration. Based on these results, we propose that CrxAl1-xN is a viable piezoelectric material whose properties can be tuned via Cr composition. We support this proposal by combinatorial synthesis experiments, which show that Cr can be incorporated in the AlN lattice up to 30% before a detectable transition to rocksalt occurs. At this Cr content, the piezoelectric modulus d33 is approximately 4 times larger than that of pure AlN. This finding, combined with the relative ease of synthesis under nonequilibrium conditions, may position CrxAl1-xN as a prime piezoelectric material for applications such as resonators and acoustic wave generators.