Abstract. The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of N sites. It is partially asymmetric in the sense that the probability of hopping left is q times the probability of hopping right. Additionally, particles may enter from the left with probability α and exit to the right with probability β.It has been observed that the (unique) stationary distribution of the PASEP has remarkable connections to combinatorics -see for example the papers of Derrida et al [8,9], Duchi and Schaeffer [11], Corteel [5], and Shapiro and Zeilberger [18]. Most recently we proved [7] that in fact the (normalized) probability of being in a particular state of the PASEP can be viewed as a certain weight generating function for permutation tableaux of a fixed shape. (This result implies the previous combinatorial results.) However, our proof relied on the matrix ansatz of Derrida et al [9], and hence did not give an intuitive explanation of why one should expect the steady state distribution of the PASEP to involve such nice combinatorics.In this paper we define a Markov chain -which we call the PT chain -on the set of permutation tableaux which projects to the PASEP, in a sense which we shall make precise. This gives a new proof of the main result of [7] which bypasses the matrix ansatz altogether. Furthermore, via the bijection of [19], the PT chain can also be viewed as a Markov chain on the symmetric group. Another nice feature of the PT chain is that it possesses a certain symmetry which extends the particle-hole symmetry of the PASEP.