  Exciton-polariton laser is a promising source of coherent light for
low-energy applications due to its low-threshold operation. However, a detailed
experimental study of its spectral purity, which directly affects its coherence
properties is still missing. Here}, we present a high-resolution spectroscopic
investigation of the energy and linewidth of an exciton-polariton laser in the
single-mode regime, which derives its coherent emission from an optically
pumped and confined exciton-polariton condensate. We report an ultra-narrow
linewidth of 56~MHz or 0.24~$\mu$eV, corresponding to a coherence time of
5.7~ns. The narrow linewidth is consistently achieved by using an
exciton-polariton condensate with a high photonic content confined in an
optically induced trap. Contrary to previous studies, we show that the
excitonic reservoir created by the pump and responsible for creating the trap
does not strongly affect the emission linewidth as long as the condensate is
trapped and the pump power is well above the condensation (lasing) threshold.
\red{The long coherence time of the exciton-polariton system uncovered here
opens up opportunities for manipulating its macroscopic quantum state, which is
essential for applications in classical and quantum computing.
