We have studied growth of c-facets in 4He crystals without screw dislocations at temperatures 2 - 200 mK. High-resolution optical interferometry allowed us to resolve interfacial speeds down to 0.01 nm/s. Contrary to expectations, c-facets were found to grow about 1 atomic layer/sec at relatively small overpressures of 0.1 mbar; this rate decreased by a factor of ten when temperature was increased from 20 mK up to 200 mK. At larger speeds, growth of c-facets consisted of consecutive bursts whose distribution in pressure displayed a strong temperature dependence. The method for measuring small rates of facet growth is described.