S duality at the black hole threshold in gravitational collapse

We study gravitational collapse of the axion-dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appears in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf., S duality). The collapse leaves behind an outgoing pulse of axion-dilaton radiation, with nearly but not exactly flat spacetime within it.