Despite fundamentally challenging in integrated (nano)photonics, achieving chip-based light nonreciprocity becomes increasingly urgent in signal processing and optical communications. Because of material incompatibilities in conventional approaches based on Faraday effects, alternative solutions have resorted to nonlinear processes to obtain one-way transmission. However, revealed dynamic reciprocity in a recent theoretical analysis has pinned down the functionalities of these nonlinear isolators. To overcome this dynamic reciprocity, we here report the first demonstration of a nonlinear optical isolator on a silicon chip enforced by phase-matched parametric amplification. Using a high-Q microtoroid resonator, we realize highly nonreciprocal transport at the 1,550 nm wavelength when waves are simultaneously launched in both forward and backward directions. Our design, compatible with current CMOS technique, yields convincing isolation performance with sufficiently low insertion loss for a wide range of input power levels. Moreover, our work evidences the possibility of designing chip-based real nonlinear isolators for information processing and laser protection.