Lead halide perovskites provide a test bed for exploring nonlinear optical properties. Although the underlying centrosymmetric crystal structure of 3D lead halide perovskites precludes the phenomenon of second harmonic generation, the third and higher-order harmonic generation are allowed. In this work, we probe the third harmonic generation (THG) from CsPbBr3 nanocrystals (NCs) and compare it to the THG from CsPbBr3 NCs with Ruddlesden-Popper planar faults (RP-CsPbBr3), formed via postsynthetic fusion-growth. The THG from CsPbBr3 NCs is negligible compared with that of RP-CsPbBr3 NCs within a wide range of femtosecond excitation wavelengths. We further compare the THG from a thin film of RP-CsPbBr3 with that of a single crystal of methylammonium lead bromide (MAPbBr3). The THG efficiency of RP-CsPbBr3 is found to be three times greater than that of MAPbBr3. An effective third-order susceptibility of the order of 10-18 m2 V-2 is obtained for a RP-CsPbBr3 film, opening up the prospect of inorganic halide perovskite NCs with planar defects for a range of nonlinear optical applications.