We present GPS++, a hybrid Message Passing Neural Network / Graph Transformer model for molecular property prediction. Our model integrates a well-tuned local message passing component and biased global attention with other key ideas from prior literature to achieve state-of-the-art results on large-scale molecular dataset PCQM4Mv2. Through a thorough ablation study we highlight the impact of individual components and, contrary to expectations set by recent trends, find that nearly all of the model's performance can be maintained without any use of global self-attention. We also show that our approach is significantly more accurate than prior art when 3D positional information is not available.