  We build optimal exponential bounds for the probabilities of large deviations
of sums \sum_{k=1}^nf(X_k) where (X_k) is a finite reversible Markov chain and
f is an arbitrary bounded function. These bounds depend only on the stationary
mean E_{\pi}f, the end-points of the support of f, the sample size n and the
second largest eigenvalue \lambda of the transition matrix.
