Species' geographic ranges are limited by climate and species interactions. Climate is the prevailing explanation for why species live only within narrow elevational ranges in megadiverse biodiverse tropical mountains, but competition can also restrict species' elevational ranges. We test contrasting predictions of these hypotheses by conducting a global comparative test of birds' elevational range sizes within 31 montane regions, using more than 4.4 million citizen science records from eBird to define species' elevational ranges in each region. We find strong support that competition, not climate, is the leading driver of narrow elevational ranges. These results highlight the importance of species interactions in shaping species' ranges in tropical mountains, Earth's hottest biodiversity hotspots.