A new preclinical PET system based on dSiPMs, called DigiPET, is presented. The system is based on thin monolithic scintillation crystals and exhibits superior spatial resolution at low-cost compared to systems based on pixelated crystals. Current dedicated small-rodent PET scanners have a spatial resolution in the order of 1 mm. Most of them have a large footprint, requiring considerable laboratory space. For rodent brain imaging, a PET scanner with sub-millimeter resolution is desired. To achieve this, crystals with a pixel pitch down to 0.5 mm have been used. However, fine pixels are difficult to produce and will render systems expensive. In this work, we present the first results with a high-resolution preclinical PET scanner based on thin monolithic scintillators and a large solid angle. The design is dedicated to rat-brain imaging and therefore has a very compact geometry. Four detectors were placed in a square arrangement with a distance of 34.5 mm between two opposing detector modules, defining a field of view (FOV) of 32 × 32 × 32 mm3. Each detector consists of a thin monolithic LYSO crystal of 32 × 32 × 2 mm3 optically coupled to a digital silicon photomultiplier (dSiPM). Event positioning within each detector was obtained using the maximum likelihood estimation (MLE) method. To evaluate the system performance, we measured the energy resolution, coincidence resolving time (CRT), sensitivity and spatial resolution. The image quality was evaluated by acquiring a hot-rod phantom filled with 18F-FDG and a rat head one hour after an 18F-FDG injection. The MLE yielded an average intrinsic spatial resolution on the detector of 0.54 mm FWHM. We obtained a CRT of 680 ps and an energy resolution of 18% FWHM at 511 keV. The sensitivity and spatial resolution obtained at the center of the FOV were 6.0 cps kBq-1 and 0.7 mm, respectively. In the reconstructed images of the hot-rod phantom, hot rods down to 0.7 mm can be discriminated. In conclusion, a compact PET scanner was built using dSiPM technology and thin monolithic LYSO crystals. Excellent spatial resolution and acceptable sensitivity were demonstrated. Promising results were also obtained in a hot-rod phantom and in rat-brain imaging.