We theoretically predict a working principle for optical amplification, based on Weyl semimetals: When a Weyl semimetal is suitably irradiated at two frequencies, electrons close to the Weyl points convert energy between the frequencies through the mechanism of topological frequency conversion from [Martin et al., Phys. Rev. X 7, 041008 (2017)]. Each electron converts energy at a quantized rate given by an integer multiple of Planck's constant multiplied by the product of the two frequencies. In simulations, we show that optimal, but feasible band structures, can support topological frequency conversion in the "THz gap" at intensities down to 2 W/mm2; the gain from the effect can exceed the dissipative loss when the frequencies are larger than the relaxation time of the system. Topological frequency conversion forms a paradigm for optical amplification, which further extends Weyl semimetals' promise for technological applications.