  How does a chemical reaction proceed at ultralow temperatures? Can simple
quantum mechanical rules such as quantum statistics, single scattering partial
waves, and quantum threshold laws provide a clear understanding for the
molecular reactivity under a vanishing collision energy? Starting with an
optically trapped near quantum degenerate gas of polar $^{40}$K$^{87}$Rb
molecules prepared in their absolute ground state, we report experimental
evidence for exothermic atom-exchange chemical reactions. When these fermionic
molecules are prepared in a single quantum state at a temperature of a few
hundreds of nanoKelvins, we observe p-wave-dominated quantum threshold
collisions arising from tunneling through an angular momentum barrier followed
by a near-unity probability short-range chemical reaction. When these molecules
are prepared in two different internal states or when molecules and atoms are
brought together, the reaction rates are enhanced by a factor of 10 to 100 due
to s-wave scattering, which does not have a centrifugal barrier. The measured
rates agree with predicted universal loss rates related to the two-body van der
Waals length.
