Despite being fundamentally challenging in integrated (nano)photonics, achieving chip-based light non-reciprocity becomes increasingly urgent in signal processing and optical communications. Because of material incompatibilities in conventional approaches based on the Faraday effect, alternative solutions have resorted to nonlinear processes to obtain one-way transmission. However, dynamic reciprocity in a recent theoretical analysis has pinned down the functionalities of these nonlinear isolators. To bypass such dynamic reciprocity, we here demonstrate an optical isolator on a silicon chip enforced by phase-matched parametric amplification in four-wave mixing. Using a high-Q microtoroid resonator, we realize highly non-reciprocal transport at the 1,550 nm wavelength when waves are injected from both directions in two different operating configurations. Our design, compatible with current complementary metal-oxide-semiconductor (CMOS) techniques, yields convincing isolation performance with sufficiently low insertion loss for a wide range of input power levels. Moreover, our work demonstrates the possibility of designing chip-based magnetic-free optical isolators for information processing and laser protection.