We search for stars with proper motions in a set of twenty deep Subaru images, covering about 0.28 square degrees to a depth of i'~25, taken over a span of six years. In this paper, we describe in detail our reduction and techniques to identify moving objects. We present a first sample of 99 stars with motions of high significance, and discuss briefly the populations from which they are likely drawn. Based on photometry and motions alone, we expect that 9 of the candidates may be white dwarfs. We also find a group of stars which may be extremely metal-poor subdwarfs in the halo.