  The dynamics of the S = 3=2 kagome antiferromagnet chromium jarosite,
KCr$_3$(OD)$_6$(SO$_4$)$_2$ 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 life-time broadening as well as a pronounced zero
mode. Using linear spin wave theory, we estimate the exchange couplings, with
the leading nearest neighbor value being $J_1$ = 0:884 meV. Above $T_N$ diffuse
excitations from cooperative paramagnetism dominate. A model for
two-dimensional magnetic cluster excitations is shown to capture the essential
features of the data in the cooperative paramagnetic phase.
