HiPERCAM is a high-speed camera for the study of rapid variability in the Universe. The project is funded by a 3.5MEuro European Research Council Advanced Grant. HiPERCAM builds on the success of our previous instrument, ULTRACAM, with very significant improvements in performance thanks to the use of the latest technologies. HiPERCAM will use 4 dichroic beamsplitters to image simultaneously in 5 optical channels covering the u'g'r'i'z' bands. Frame rates of over 1000 per second will be achievable using an ESO CCD controller (NGC), with every frame GPS timestamped. The detectors are custom-made, frame-transfer CCDs from e2v, with 4 low-noise (2.5e-) outputs, mounted in small thermoelectrically-cooled heads operated at 180 K, resulting in virtually no dark current. The two reddest CCDs will be deep-depletion devices with anti-etaloning, providing high quantum efficiencies across the red part of the spectrum with no fringing. The instrument will also incorporate scintillation noise correction via the conjugate-plane photometry technique. The opto-mechanical chassis will make use of additive manufacturing techniques in metal to make a light-weight, rigid and temperature-invariant structure. First light is expected on the 4.2m William Herschel Telescope on La Palma in 2017 (on which the field of view will be 10' with a 0.3"/pixel scale), with subsequent use planned on the 10.4m Gran Telescopio Canarias on La Palma (on which the field of view will be 4' with a 0.11"/pixel scale) and the 3.5m New Technology Telescope in Chile.