A Compton camera-based detector system for photon detection from nuclear reactions induced by proton (or heavier ion) beams is under development at LMU Munich, targeting the online range verification of the particle beam in hadron therapy via prompt-gamma imaging. The detector is designed to be capable to reconstruct the photon source origin not only from the Compton scattering kinematics of the primary photon, but also to allow for tracking of the secondary Compton-scattered electrons, thus enabling a γ-source reconstruction also from incompletely absorbed photon events. The Compton camera consists of a monolithic LaBr₃:Ce scintillation crystal, read out by a multi-anode PMT acting as absorber, preceded by a stacked array of 6 double-sided silicon strip detectors as scatterers. The detector components have been characterized both under offline and online conditions. The LaBr₃:Ce crystal exhibits an excellent time and energy resolution. Using intense collimated ¹³⁷Cs and ⁶⁰Co sources, the monolithic scintillator was scanned on a fine 2D grid to generate a reference library of light amplitude distributions that allows for reconstructing the photon interaction position using a k-Nearest Neighbour (k-NN) algorithm. Systematic studies were performed to investigate the performance of the reconstruction algorithm, revealing an improvement of the spatial resolution with increasing photon energy to an optimum value of 3.7(1)mm at 1.33 MeV, achieved with the Categorical Average Pattern (CAP) modification of the k-NN algorithm.