Treefall gaps are hypothesized to maintain diversity by creating resource-rich, heterogeneous habitats necessary for species coexistence. This hypothesis, however, is not supported empirically for shade-tolerant trees, the dominant plant group in tropical forests. The failure of gaps to maintain shade-tolerant trees remains puzzling, and the hypothesis implicated to date is dispersal limitation. In central Panama, we tested an alternative 'biotic interference' hypothesis: that competition between growth forms (lianas vs. trees) constrains shade-tolerant tree recruitment, survival and diversity in gaps. We experimentally removed lianas from eight gaps and monitored them for 8 years, while also monitoring nine un-manipulated control gaps. Removing lianas increased tree growth, recruitment and richness by 55, 46 and 65%, respectively. Lianas were particularly harmful to shade-tolerant species, but not pioneers. Our findings demonstrate that competition between plant growth forms constrains diversity in a species-rich tropical forest. Because lianas are abundant in many tropical systems, our findings may apply broadly.