The single-crystal elastic moduli of chromium have been measured ultrasonically to 5 kbar and from 80 to 700K. In the paramagnetic phase the shear moduli are found to be approximately linear functions of pressure and temperature for pressures and temperatures above the Neel transition line. At atmospheric pressure, the compressional modulus C₁₁ increases with temperature above T_N up to a maximum at about 475K, and then decreases and becomes a linear function of T above 550K.C₁₁ is not a linear function P for temperatures up to 473K. The results for paramagnetic chromium are combined with previous results on Ti-V and V-Cr alloys to discuss the relationship of the elastic properties to the electronic bandstructure of these alloys.