Inelastic neutron scattering measurements were carried out on the Ti50Pd50-xCrx alloy, which has the potential for being a high temperature shape memory material. For x=0, the transformation temperature is ~800K and for the composition studied (x=8 at.%) TM ~ 400K. The majority of the measurements were performed in the parent, β-phase, up to 873K. Most of the phonons propagating along the three symmetry directions [ζ00], [ζζζ], and [ζζ0] were well defined with the exception of the [ζζ0] transverse acoustic mode with displacements along the [-ζζ0] corresponding to the C’=1/2(C11-C12) elastic constant. These phonons are well defined for small ζ, but for ζ > 0.15 they are strongly overdamped near the transition temperature, but become better defined at higher temperatures. An elastic peak develop in the cubic phase at ζ=0.22 and increases in intensity as TM is approached. However, the dispersion curves show no anomaly at this particular wavevector, in marked contrast to the lattice dynamic studies of other systems exhibiting Martensitic transformations.