  Motivated by recent experiments we derive an exact expression for the
correlation function entering the three-body recombination rate for a
one-dimensional gas of interacting bosons. The answer, given in terms of two
thermodynamic parameters of the Lieb-Liniger model, is valid for all values of
the dimensionless coupling $\gamma$ and contains the previously known results
for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also
investigate finite-size effects by calculating the correlation function for
small systems of 3, 4, 5 and 6 particles.
