  We derive an exact analytic expression for the three-body local correlations
in the Lieb-Liniger model of 1D Bose gas with contact repulsion. The local
three-body correlations control the thermalization and particle loss rates in
the presence of terms which break integrability, as is realized in the case of
1D ultracold bosons. Our result is valid not only at finite temperature but
also for a large class of non-thermal excited states in the thermodynamic
limit. We present finite temperature calculations in the presence of external
harmonic confinement within local density approximation, and for a highly
excited state that resembles an experimentally realized configuration.
