We present the results of muon-spin relaxation measurements on the triangular lattice Heisenberg antiferromagnet $alpha$-KCrO$_{2}$. We observe sharp changes in behaviour at an ordering temperature of $T_{mathrm{c}}=23$ K, with an additional broad feature in the muon-spin relaxation rate evident at T=13 K, both of which correspond to features in the magnetic contribution to the heat capacity. This behaviour is distinct from both the Li- and Na- containing members of the series. These data may be qualitatively described with the established theoretical predictions for the underlying spin system.