Bulk chromium triiodide (CrI$_3$) has long been known as a layered van der Waals ferromagnet. However, its monolayer form was only recently isolated and confirmed to be a truly two-dimensional (2D) ferromagnet, providing a new platform for investigating light-matter interactions and magneto-optical phenomena in the atomically thin limit. Here, we report spontaneous circularly polarized photoluminescence in monolayer CrI$_3$ under linearly polarized excitation, with helicity determined by the monolayer magnetization direction. In contrast, the bilayer CrI$_3$ photoluminescence exhibits vanishing circular polarization, supporting the recently uncovered anomalous antiferromagnetic interlayer coupling in CrI$_3$ bilayers. Distinct from the Wannier-Mott excitons that dominate the optical response in well-known 2D van der Waals semiconductors, our absorption and layer-dependent photoluminescence measurements reveal the importance of ligand-field and charge-transfer transitions to the optoelectronic response of atomically thin CrI$_3$. We attribute the photoluminescence to a parity-forbidden d-d transition characteristic of Cr$^{3+}$ complexes, which displays broad linewidth due to strong vibronic coupling and thickness-independent peak energy due to its localized molecular orbital nature.