Ultracold polyatomic molecules have potentially wide-ranging applications in quantum simulation and computation, particle physics, and quantum chemistry. For atoms and small molecules, direct laser cooling has proven to be a powerful tool for quantum science in the uftracold regime. However, the feasibility of laser-cooling larger, nonlinear polyatomic molecules has remained unknown because of their complex structure. We laser-cooled the symmetric top molecule calcium monomethoxide (CaOCH3), reducing the temperature of similar to 10(4) molecules from 22 +/- 1 millikelvin to 1.8 +/- 0.7 millikelvin in one dimension and state-selectively cooling two nuclear spin isomers. These results demonstrate that the use of proper rovibronic transitions enables laser cooling of nonlinear molecules, thereby opening a path to efficient cooling of chiral molecules and, eventually, optical tweezer arrays of complex polyatomic species.