The thermal conductivity of iron-based superconductor CsFe$_2$As$_2$ single crystal ($T_c =$ 1.81 K) was measured down to 50 mK. A significant residual linear term $kappa_0/T$ = 1.27 mW K$^{-2}$ cm$^{-1}$ is observed in zero magnetic field, which is about 1/10 of the normal-state value in upper critical field $H_{c2}$. In low magnetic field, $kappa_0/T$ increases rapidly with field. The overall field dependence of $kappa_0/T$ for our CsFe$_2$As$_2$ (with residual resistivity $rho_0$ = 1.80 $muOmega$ cm) lies between the dirty KFe$_2$As$_2$ (with $rho_0$ = 3.32 $muOmega$ cm) and the clean KFe$_2$As$_2$ (with $rho_0$ = 0.21 $muOmega$ cm). These results strongly suggest nodal superconducting gap in CsFe$_2$As$_2$, similar to its sister compound KFe$_2$As$_2$.
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