The S=3/2 zigzag chain antiferromagnet beta-CaCr2O4 exhibits broad spinwave excitations at low temperature, related to an incommensurate magnetic order that sets at TN = 21K. However, an excitation spectrum characterized by an unusual broad signal persists well above TN, and is thought to arise from the contribution of a two-spinon continuum. Recently, a large single crystal was successfully synthesized and we would like to study and fully characterize the spin dynamics, especially in the low temperature regime, in order to determine the spin Hamiltonian of this system.