Few-shot class incremental learning---the problem of updating a trained classifier to discriminate among an expanded set of classes with limited labeled data---is a key challenge for machine learning systems deployed in non-stationary environments. Existing approaches to the problem rely on complex model architectures and training procedures that are difficult to tune and re-use. In this paper, we present an extremely simple approach that enables the use of ordinary logistic regression classifiers for few-shot incremental learning. The key to this approach is a new family of \emph{subspace regularization} schemes that encourage weight vectors for new classes to lie close to the subspace spanned by the weights of existing classes. When combined with pretrained convolutional feature extractors, logistic regression models trained with subspace regularization outperform specialized, state-of-the-art approaches to few-shot incremental image classification by up to 22\% on the \textit{mini}ImageNet dataset. Because of its simplicity, subspace regularization can be straightforwardly extended to incorporate additional background information about the new classes (including class names and descriptions specified in natural language); these further improve accuracy by up to 2\%. Our results show that simple geometric regularization of class representations offer an effective tool for continual learning.