We report a silicon-based integrated optical sampling chip. High-repetition-rate optical sampling pulses are generated by interleaving low-repetition-rate input optical pulses with the assistance of wavelength-division multiplexing (WDM) and mode-division multiplexing (MDM). The WDM pulse interleaver is based on a loopback arrayed waveguide grating (AWG) with linearly increasing delays. The amplitude of the interleaved pulses can be adjusted by the attenuators in the loopback waveguides. Two high-order modes in a multimode waveguide are utilized to further increase the pulse repetition rate. With WDM and MDM, the optical pulse sampling rate is increased by 8 times. The optical sampling pulses are then modulated by a multimode Mach-Zehnder modulator with the active arms integrated with L-shaped PN junctions. The sampled pulses are finally separated by mode and wavelength demultiplexers for low-speed parallel processing. The wavelength demultiplexer is made of a dual-ring assisted Mach-Zehnder interferometer (DR-MZI) with high wavelength selectivity. This successful implementation of the high-speed sampling chip marks a significant step forward in the full integration of analog-to-digital converters on a single chip and opens up avenues toward real applications of microwave photonics.