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We consider the problem of a semiclassical description of quantum chaotictransport, when a tunnel barrier is present in one of the leads. Using asemiclassical approach formulated in terms of a matrix model, we obtaintransport moments as power series in the reflection probability of the barrier,whose coefficients are rational functions of the number of open channels M. Ourresults are therefore valid in the quantum regime and not only when $M\gg 1$.The expressions we arrive at are not identical with the correspondingpredictions from random matrix theory, but are in fact much simpler. Boththeories agree as far as we can test.

Semiclassical treatment of quantum chaotic transport with a tunnel barrier