Many protocols are designed to operate correctly even in the case where the underlying communication medium is faulty. To capture the behaviour of such protocols, lossy channel systems (LCS) have been proposed. In an LCS the communication channels are modelled as FIFO buffers which are unbounded, but also unreliable in the sense that they can nondeterministically lose messages. Recently, several attempts have been made to study probabilistic lossy channel systems (PLCS) in which the probability of losing messages is taken into account and the following qualitative model checking problem is investigated: to verify whether a given property holds with probability one. Here we consider a more challenging problem, namely to calculate the probability by which a certain property is satisfied. Our main result is an algorithm for the following Quantitative model checking problem: Instance: A PLCS, its state s, a finite state ω-automaton A, and a rational θ>0. Task: Find a rational r such that the probability of the set of computations that start at s and are accepted by A is between r and r+θ.