Text classifiers are regularly applied to personal texts, leaving users of these classifiers vulnerable to privacy breaches. We propose a solution for privacy-preserving text classification that is based on Convolutional Neural Networks (CNNs) and Secure Multiparty Computation (MPC). Our method enables the inference of a class label for a personal text in such a way that (1) the owner of the personal text does not have to disclose their text to anyone in an unencrypted manner, and (2) the owner of the text classifier does not have to reveal the trained model parameters to the text owner or to anyone else. To demonstrate the feasibility of our protocol for practical private text classification, we implemented it in the PyTorch-based MPC framework CrypTen, using a well-known additive secret sharing scheme in the honest-but-curious setting. We test the runtime of our privacy-preserving text classifier, which is fast enough to be used in practice.