Laser cooling and trapping and magneto-optical trapping methods in particular, have enabled groundbreaking advances in science, including Bose–Einstein condensation, quantum computation with neutral atoms6,7and high-precision optical clocks. Recently, magneto-optical traps (MOTs) of diatomic molecules have been demonstrated, providing access to research in quantum simulation13and searches for physics beyond the standard model. Compared with diatomic molecules, polyatomic molecules have distinct rotational and vibrational degrees of freedom that promise a variety of transformational possibilities. For example, ultracold polyatomic molecules would be uniquely suited to applications in quantum computation and simulation, ultracold collisions, quantum chemistry and beyond-the-standard-model searches. However, the complexity of these molecules has so far precluded the realization of MOTs for polyatomic species. Here we demonstrate magneto-optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). After trapping, the molecules are laser cooled in a blue-detuned optical molasses to a temperature of 110 μK, which is below the Doppler cooling limit. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including quantum simulation and computation using optical tweezer arrays. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomic species will be both feasible and practical.