Buffer gas cooling is used to trap NH molecules with 1/e lifetimes exceeding 20 s. Helium vapor generated by laser desorption of a helium film is employed to thermalize 10(5) molecules at a temperature of 500 mK in a 3.9 T magnetic trap. Long molecule trapping times are attained through rapid pumpout of residual buffer gas. Molecules experience a helium background gas density below 1 x 10(12) cm(-3).