As a first step towards the goal of achieving Bose-Einstein condensation of orthopositronium (o-Ps), we have been pursuing laser cooling using an ultraviolet laser. It is essential in the laser cooling to produce a large number of the o-Ps with the lowest possible temperature. This paper describes the laser cooling system in terms of an o-Ps production facility and a special Cr:LiSAF laser having been developed so far and experimental results of thermal o-Ps production.