We propose the use of a Transformer to accurately predict normals from point clouds with noise and density variations. Previous learning-based methods utilize PointNet variants to explicitly extract multi-scale features at different input scales, then focus on a surface fitting method by which local point cloud neighborhoods are fitted to a geometric surface approximated by either a polynomial function or a multi-layer perceptron (MLP). However, fitting surfaces to fixed-order polynomial functions can suffer from overfitting or underfitting, and learning MLP-represented hyper-surfaces requires pre-generated per-point weights. To avoid these limitations, we first unify the design choices in previous works and then propose a simplified Transformer-based model to extract richer and more robust geometric features for the surface normal estimation task. Through extensive experiments, we demonstrate that our Transformer-based method achieves state-of-the-art performance on both the synthetic shape dataset PCPNet, and the real-world indoor scene dataset SceneNN, exhibiting more noise-resilient behavior and significantly faster inference. Most importantly, we demonstrate that the sophisticated hand-designed modules in existing works are not necessary to excel at the task of surface normal estimation.