A continuously operated electrostatic trap for polar molecules is demonstrated. The trap has a volume of approximately 0.6 cm3 and holds molecules with a positive Stark shift. With deuterated ammonia from a quadrupole velocity filter, a trap density of approximately 10(8) cm(-3) is achieved with an average lifetime of 130 ms and a motional temperature of approximately 300 mK. The trap offers good starting conditions for high-precision measurements, and can be used as a first stage in cooling schemes for molecules and as a "reaction vessel" in cold chemistry.