Optical parametric amplification is a second-order nonlinear process whereby an optical signal is amplified by a pump via the generation of an idler field'. This mechanism is inherently related to spontaneous parametric down-conversion, which currently constitutes the building block for entangled photon pair generations(2), a process that is exploited in modern quantum technologies. Here we demonstrate single-pass optical parametric amplification at the ultimate thickness limit; using semiconducting transition metal dichalcogenides(3,4), we show that amplification can be attained over propagation through a single atomic layer. Such a second-order nonlinear interaction at the two-dimensional limit bypasses phase-matching requirements(5) and achieves ultrabroad amplification bandwidths. In agreement with first-principle calculations, we observe that the amplification process is independent of the in-plane polarization of signal and pump fields. By the use of AA-stacked multilayers, we present a clear pathway towards the scaling of conversion efficiency. Our results pave the way for the development of atom-sized tunable sources of radiation with potential applications in nanophotonics and quantum information technology.