Spiking Neural Networks (SNNs) remain on the fringe of machine learning research despite their potential for fast low-power performance and fully local operation, including rapid online learning, on edge computing devices. In SNNs, encoding information in the timing of individual spikes is more efficient than using spiking rates for which many spikes are required. However, combining spike-time coding with unsupervised learning has proven somewhat challenging. Here we use spike latency coding with local unsupervised spike-timing-dependent plasticity and several biologically inspired local homeostatic mechanisms that maintain network stability. We show that when trained on sequences of characters from text, the network rapidly and effectively self-organizes to learn a latent space mapping of character attributes, similar to word2vec but for characters (i.e. char2vec), forming clusters of vowels, consonants and punctuation for example. It does so with no explicit objective function and no error signal, showing that time-encoded unsupervised SNNs (STUNNs) can maintain dynamical stability while self-organizing to extract complex input relationships using only local learning rules.