A modular gamma ray camera is described that gives useful image information over its entire crystal face. The lack of dead area on the periphery of the camera is made possible by a unique application of digital electronics and optimal position estimation using maximum likelihood (ML) estimates. The ML estimates are calculated directly from photomultiplier tube responses and stored in a lookup table, so the restriction of calculating the position estimates in separate circuitry is removed. Each module is designed to be optically and electronically independent, so that many modules can be combined in a large system. Results from a prototypical module, which has an active crystal area of 10 cm X 10 cm, are presented.