This paper presents a methodology to speed up the stationary analysis of large Markov chains that model asynchronous systems. Instead of directly working on the original Markov chain, we propose to analyze a smaller Markov chain obtained via a novel technique called string-based state compression. Once the smaller chain is solved, the solution to the original chain is obtained via a process called expansion. The method is especially powerful when the Markov chain has a small feedback vertex set, which happens often in asynchronous systems. Experimental results show that the method can yield reductions of more than an order of magnitude in run time and facilitate the analysis of larger systems than possible using traditional techniques.