We report optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). CaOH molecules from a magneto-optical trap are sub-Doppler laser cooled to $20(3)$ µK in free space and loaded into an optical dipole trap. We attain an in-trap molecule number density of $3(1)\times 10^9$ cm$^{-3}$ at a temperature of $57(8)$ µK. Trapped CaOH molecules are optically pumped into an excited vibrational bending mode, whose $\ell$-type parity doublet structure is a potential resource for a wide range of proposed quantum science applications with polyatomic molecules. We measure the spontaneous, radiative lifetime of this bending mode state to be ~0.7s.