Decision trees are a powerful prediction model with many applications in statistics, data mining, and machine learning. In some settings, the model and the data to be classified may contain sensitive information belonging to different parties. In this paper, we, therefore, address the problem of privately evaluating a decision tree on private data. This scenario consists of a server holding a private decision tree model and a client interested in classifying its private attribute vector using the server's private model. The goal of the computation is to obtain the classification while preserving the privacy of both - the decision tree and the client input. After the computation, the classification result is revealed only to the client, and nothing else is revealed neither to the client nor to the server. Existing privacy-preserving protocols that address this problem use or combine different generic secure multiparty computation approaches resulting in several interactions between the client and the server. Our goal is to design and implement a novel client-server protocol that delegates the complete tree evaluation to the server while preserving privacy and reducing the overhead. The idea is to use fully (somewhat) homomorphic encryption and evaluate the tree on ciphertexts encrypted under the client's public key. However, since current somewhat homomorphic encryption schemes have high overhead, we combine efficient data representations with different algorithmic optimizations to keep the computational overhead and the communication cost low. As a result, we are able to provide the first non-interactive protocol, that allows the client to delegate the evaluation to the server by sending an encrypted input and receiving only the encryption of the result. Our scheme has only one round and can evaluate a complete tree of depth 10 within seconds.