We measured the temperature dependence of the surface impedance Zs - Rs + iXs at 9.6 and 14 GHz in a single crystal of the Kondo lattice compound CeNiSn, from which microwave complex conductivity σ(T) = σ1(T) - iσ2(T) was determined. Below about 10 K the imaginary part σ2 increases rapidly and the real part σ1 is much lower than the dc conductivity. These results indicate a rapid decrease in the scattering rate of the quasiparticles, whose excitation spectrum is drastically changed with the coherence gap formation at low temperatures.