  We report the first demonstration of cooling by three-body losses in a Bose
gas. We use a harmonically confined one-dimensional (1D) Bose gas in the
quasi-condensate regime and, as the atom number decreases under the effect of
three-body losses, the temperature $T$ drops up to a factor four. The ratio
$k_B T/(m c^2)$ stays close to 0.64, where $m$ is the atomic mass and $c$ the
sound speed in the trap center. The dimensionless 1D interaction parameter
$\gamma$, evaluated at the trap center, spans more than two order of magnitudes
over the different sets of data. We present a theoretical analysis for a
homogeneous 1D gas in the quasi-condensate regime, which predicts that the
ratio $k_B T/(mc^2)$ converges towards 0.6 under the effect of three-body
losses. More sophisticated theoretical predictions that take into account the
longitudinal harmonic confinement and transverse effects are in agreement
within 30% with experimental data.
