Silicon photomultipliers (SiPMs) are of great interest to positron emission tomography (PET), as they enable new detector geometries, for e. g., depth-of-interaction (DOI) determination, are MR compatible, and offer faster response and higher gain than other solid-state photosensors such as avalanche photodiodes. Here we present a novel detector design with DOI correction, in which a position-sensitive SiPM array is used to read out a monolithic scintillator. Initial characterization of a prototype detector consisting of a 4 x 4 SiPM array coupled to either the front or back surface of a 13.2 mm x 13.2 mm x 10 mm LYSO: Ce(3+) crystal shows that front-side readout results in significantly better performance than conventional back-side readout. Spatial resolutions <1.6 mm full-width-at-half-maximum (FWHM) were measured at the detector centre in response to an similar to 0.54 mm FWHM diameter test beam. Hardly any resolution losses were observed at angles of incidence up to 45 degrees, demonstrating excellent DOI correction. About 14% FWHM energy resolution was obtained. The timing resolution, measured in coincidence with a BaF(2) detector, equals 960 ps FWHM.