There are many well-known concentration results for sums of independent random matrices, e.g. those of Rudelson, Ahlswede-Winter, Tropp, and Oliveira. We move beyond the independent setting, and prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an reversible Markov chain, confirming a conjecture due to Wigderson and Xiao. Our proof is based on a new multi-matrix extension of the Golden-Thompson inequality which follows from complex interpolation methods. Joint work with A. Garg, Y. Lee, and Z. Song.