The collective excitations in magnetic materials, i.e. spin waves or magnons, may couple to inelastically scattered light. Despite the recent interest in two-dimensional (2D) van der Waals magnets, a direct observation of magnons in the monolayer limit is lacking. Here, we report the observation of 2D magnons in atomically thin CrI₃ by magneto-optical Raman measurements. In monolayer and bilayer CrI₃, we observe a sharp one-magnon feature at a zero-field energy of ~.3 meV which blue-shifts with a g factor of 2. However, at the metamagnetic transition from the layered antiferromagnetic to spin-polarized state in bilayer, the magnon exhibits a discontinuous red-shift. This confirms that the magnetic anisotropy is much larger than the interlayer exchange in CrI₃. In addition, we observe a magnon feature at ~19 meV (~ 4.6 THz) for bilayer and thicker samples, significantly higher than Γ point magnons in standard ferromagnetic systems, i.e. YIG. Our results establish CrI₃ as a potential candidate in miniaturized terahertz magnonic devices.