In this work we propose a high resolution, compact gamma ray imager, to be used in medical imaging applications. It is based on a monolithic array of silicon drift detectors (SDDs), with an active area of 6.7 cm2, coupled to a single scintillator crystal, according to the Anger Camera principle: when a gamma photon is detected, the scintillation light is shared among several pixels. The position of interaction is obtained subsequently via a centroid identification algorithm. The use of an array of low noise SDDs, optimizes the spatial resolution of the system, expected to be below 1 mm FWHM. The analog front-end electronics for the readout of the complete array is composed of ten 8-channels ASICs, each one featuring a low noise preamplifier, a 6th order semigaussian shaper, a peak stretcher and an analog multiplexer. A digital section of the ASIC provides the multiplexer management and the self-resetting of each analog channel. The signals are then converted by a 50 Ms/s acquisition board, connected via a USB 2.0 interface to the host PC, where a custom centroid identification algorithm is implemented. In this work we present a description of the system and the first results of its experimental characterization.