Event cameras are gaining popularity due to their unique properties, such as their low latency and high dynamic range. One task where these benefits can be crucial is real-time object detection. However, RGB detectors still outperform event-based detectors due to the sparsity of the event data and missing visual details. In this paper, we develop a novel knowledge distillation approach to shrink the performance gap between these two modalities. To this end, we propose a cross-modality object detection distillation method that by design can focus on regions where the knowledge distillation works best. We achieve this by using an object-centric slot attention mechanism that can iteratively decouple features maps into object-centric features and corresponding pixel-features used for distillation. We evaluate our novel distillation approach on a synthetic and a real event dataset with aligned grayscale images as a teacher modality. We show that object-centric distillation allows to significantly improve the performance of the event-based student object detector, nearly halving the performance gap with respect to the teacher.