  An effective field theory for the three-body system with large scattering
length a is applied to three-body recombination into deep bound states in a
Bose gas. The recombination constant \alpha is calculated to first order in the
short-distance interactions that allow the recombination. For a < 0, the
dimensionless combination m \alpha/(\hbar a^4) is a periodic function of \ln
|a| that exhibits resonances at values of a that differ by multiplicative
factors of 22.7. This dramatic behavior should be observable near a Feshbach
resonance when a becomes large and negative.
