Single crystals of the high temperature ceramic boron carbide have been synthesized by the optical floating zone method. Room temperature elastic constants of a carbon-deficient boron carbide single crystal have been measured using the resonant ultrasound spectroscopy technique. Based upon density measurements, the single crystal stoichiometry was specified as B5.6C. This crystal has room temperature single crystal elastic constants of c(11) = 542.81, c(33) = 534.54, c(13) = 63.51, c(12) = 130.59, and c(44) = 164.79 GPa, respectively. Analysis of Cauchy's relationships, Poisson's ratios, and elastic anisotropic factors for the single crystal elastic constants indicates that it is more strongly anisotropic in elasticity and interatomic bonding than most solids. Room temperature isotropic elastic moduli of boron carbide show that its bulk, shear and Young's moduli are substantially higher than those of most solids, so that boron carbide belongs to the so-called "strong solids". Its Poisson's ratio is significantly lower than that of most solids.