We have investigated the structural and magnetic properties of S=3/2Cr3+ Heisenberg-like kagome lattice antiferromagnets Cs2KCr3F12 and Cs2NaCr3F12 using single crystals. Each compound has a slightly distorted kagome lattice, although the space groups differ for the two compounds. The magnetic data suggest that each compound exhibits the formation of antiferromagnetic ordering with in-plane-spin canting approximately below 6 K. The in-plane coplanar structures are clearly different from disordered ground states of the isostructural Ti3+ compounds and out-of-plane coplanar structures of the V3+ compounds, which is mainly caused by the differences in the strength of quantum fluctuation and the strength of magnetic anisotropy for these three spin systems. In contrast, as well as the Ti3+ and V3+ compounds, the magnetization curves show 1/3-magnetization-plateaulike anomalies.