The dynamics of the S = 3/2 kagome antiferromagnet chromium jarosite, KCr3(OD)(6)(SO4)(2), was studied using high-resolution neutron time-of-flight spectroscopy on a polycrystalline sample with a nearly stoichiometric magnetic lattice [2.8(2)% Cr vacancies]. Neutron spectroscopy reveals diffuse spin wave excitations in the ordered phase with an incomplete gap and significant finite-lifetime broadening as well as a pronounced kagome zero mode. Using linear spin wave theory, we estimate the exchange couplings. The system is highly two dimensional with the leading nearest-neighbor coupling being J(1) = 0.881 meV. Above T-N, diffuse excitations from the classical spin liquid regime dominate. We model the Q response and energy response separately and show that in both the ordered phase and the classical spin liquid regime they are strongly coupled.