  We study tunneling in various shaped, closed, two-dimensional, flat
potential, double wells by calculating the energy splitting between symmetric
and anti-symmetric state pairs. For shapes that have regular or nearly regular
classical behavior (e.g. rectangular or circular) the tunneling rates vary
greatly over wide ranges often by several orders of magnitude. However, for
well shapes that admit more classically chaotic behavior (e.g. the stadium, the
Sinai billiard) the range of tunneling rates narrows, often by orders of
magnitude. This dramatic narrowing appears to come from destabilization of
periodic orbits in the regular wells that produce the largest and smallest
tunneling rates and causes the splitting vs. energy relation to take on a
possibly universal shape. It is in this sense that we say the quantum chaos
regularizes the tunneling rates.
