We developed a highly sensitive, reliable and portable automatic system (H3) to monitor the radon concentration of the underground experimental halls of the Daya Bay Reactor Neutrino Experiment. H3 is able to measure radon concentration with a statistical error less than 10% in a 1-h measurement of dehumidified air (R.H. 5% at 25°C) with radon concentration as low as 50 Bq/m3. This is achieved by using a large radon progeny collection chamber, semiconductor α-particle detector with high energy resolution, improved electronics and software. The integrated radon monitoring system is highly customizable to operate in different run modes at scheduled times and can be controlled remotely to sample radon in ambient air or in water from the water pools where the antineutrino detectors are being housed. The radon monitoring system has been running in the three experimental halls of the Daya Bay Reactor Neutrino Experiment since November 2013.