The momentum distribution of positronium (Ps) in the free space between silica aerogel grains filled with gaseous O₂ has been measured as a function of O₂ pressure. It reveals that para-Ps with kinetic energy >or approximately=1 eV is efficiently slowed down. This is attributed to successive triplet to or from singlet conversions of the Ps through inelastic collisions with O₂. The cross section for this process is estimated to be at least two orders of magnitude larger than that for the conversion through elastic collisions.