Localization of wireless transmitters based on channel state information (CSI) fingerprinting finds widespread use in indoor as well as outdoor scenarios. Fingerprinting localization first builds a database containing CSI with measured location information. One then searches for the most similar CSI in this database to approximate the position of wireless transmitters. In this paper, we investigate the efficacy of locality-sensitive hashing (LSH) to reduce the complexity of the nearest neighbor-search (NNS) required by conventional fingerprinting localization systems. More specifically, we propose a low-complexity and memory efficient LSH function based on the sum-to-one (STOne) transform and use approximate hash matches. We evaluate the accuracy and complexity (in terms of the number of searches and storage requirements) of our approach for line-of-sight (LoS) and non-LoS channels, and we show that LSH enables low-complexity fingerprinting localization with comparable accuracy to methods relying on exact NNS or deep neural networks.