  Finding and sampling rare trajectories in dynamical systems is a difficult
computational task underlying numerous problems and applications. In this paper
we show how to construct Metropolis- Hastings Monte Carlo methods that can
efficiently sample rare trajectories in the (extremely rough) phase space of
chaotic systems. As examples of our general framework we compute the
distribution of finite-time Lyapunov exponents (in different chaotic maps) and
the distribution of escape times (in transient-chaos problems). Our methods
sample exponentially rare states in polynomial number of samples (in both low-
and high-dimensional systems). An open-source software that implements our
algorithms and reproduces our results can be found in
https://github.com/jorgecarleitao/chaospp
