We describe the design and expected performance of Clover, a new instrument designed to measure the B-mode polarization of the cosmic microwave background. The proposed instrument will comprise three independent telescopes operating at 90, 150 and 220 GHz and is planned to be sited at Dome C, Antarctica. Each telescope will feed a focal plane array of 128 background-limited detectors and will measure polarized signals over angular multipoles 20 < l < 1000. The unique design of the telescope and careful control of systematics should enable the B-mode signature of gravitational waves to be measured to a lensing-confusion-limited tensor-to-scalar ratio r~0.005.