  21 cm intensity mapping has arisen as a powerful probe of the high-redshift
universe, but its potential is limited by extremely bright foregrounds and high
source confusion. In this Letter, we propose a new analysis which can help
solve both problems. From the combination of an intensity map with an
overlapping galaxy survey we construct a new one-point statistic which is
unbiased by foregrounds and contains information left out of conventional
analyses. We show that our method can measure the HI mass function with
unprecedented precision using observations similar to recent 21 cm detections.
