With the realization of faster telecommunication data rates and an expanding interest in ultrafast chemical and physical phenomena, it has become important to develop techniques that enable simple measurements of optical waveforms with subpicosecond resolution. State-of-the-art oscilloscopes with high-speed photodetectors provide single-shot waveform measurement with 30-ps resolution. Although multiple-shot sampling techniques can achieve few-picosecond resolution, single-shot measurements are necessary to analyse events that are rapidly varying in time, asynchronous, or may occur only once. Further improvements in single-shot resolution are challenging, owing to microelectronic bandwidth limitations. To overcome these limitations, researchers have looked towards all-optical techniques because of the large processing bandwidths that photonics allow. This has generated an explosion of interest in the integration of photonics on standard electronics platforms, which has spawned the field of silicon photonics and promises to enable the next generation of computer processing units and advances in high-bandwidth communications. For the success of silicon photonics in these areas, on-chip optical signal-processing for optical performance monitoring will prove critical. Beyond next-generation communications, silicon-compatible ultrafast metrology would be of great utility to many fundamental research fields, as evident from the scientific impact that ultrafast measurement techniques continue to make. Here, using time-to-frequency conversion via the nonlinear process of four-wave mixing on a silicon chip, we demonstrate a waveform measurement technology within a silicon-photonic platform. We measure optical waveforms with 220-fs resolution over lengths greater than 100 ps, which represent the largest record-length-to-resolution ratio (>450) of any single-shot-capable picosecond waveform measurement technique. Our implementation allows for single-shot measurements and uses only highly developed electronic and optical materials of complementary metal-oxide-semiconductor (CMOS)-compatible silicon-on-insulator technology and single-mode optical fibre. The mature silicon-on-insulator platform and the ability to integrate electronics with these CMOS-compatible photonics offer great promise to extend this technology into commonplace bench-top and chip-scale instruments.