A type of bound states of solitons in a passively mode-locked fibre soliton laser was experimentally observed. The observed bound states of solitons are characterized as being very stable, and have discrete, fixed soliton separations. Comparing the pulse separation of the bound solitons with that of the individual soliton pulse duration, it was shown that the formation of the observed bound solitons is due to a direct interaction between the solitons in the laser.