Projected demands in information bandwidth have resulted in a paradigm shift from electrical to optical interconnects. Switches, modulators and wavelength converters have all been demonstrated on complementary metal-oxide semiconductor compatible platforms, and are important for all optical signal and information processing. Similarly, pulse compression is crucial for creating short pulses necessary for key applications in high-capacity communications, imaging and spectroscopy. In this study, we report the first demonstration of a chip-scale, nanophotonic pulse compressor on silicon, operating by nonlinear spectral broadening from self-phase modulation in a nanowire waveguide, followed by temporal compression with an integrated dispersive element. Using a low input peak power of 10 W, we achieve compression factors as high as 7 for 7 ps pulses. This compact and efficient device will enable ultrashort pulse sources to be integrated with systems level photonic circuits necessary for future optoelectronic networks.