Deconstruction of the cellulose in plant cell walls is critical for carbon flow through ecosystems and for the production of sustainable cellulosic biofuels. Our understanding of cellulose deconstruction is largely limited to the study of microbes in isolation, but in nature, this process is driven by microbes within complex communities. In Neotropical forests, microbes in leaf-cutter ant refuse dumps are important for carbon turnover. These dumps consist of decaying plant material and a diverse bacterial community, as shown here by electron microscopy. To study the portion of the community capable of cellulose degradation, we performed enrichments on cellulose using material from five Atta colombica refuse dumps. The ability of enriched communities to degrade cellulose varied significantly across refuse dumps. 16S rRNA gene amplicon sequencing of enriched samples identified that the community structure correlated with refuse dump and with degradation ability. Overall, samples were dominated by Bacteroidetes, Gammaproteobacteria, and Betaproteobacteria. Half of abundant operational taxonomic units (OTUs) across samples were classified within genera containing known cellulose degraders, including Acidovorax, the most abundant OTU detected across samples, which was positively correlated with cellulolytic ability. A representative Acidovorax strain was isolated, but did not grow on cellulose alone. Phenotypic and compositional analyses of enrichment cultures, such as those presented here, help link community composition with cellulolytic ability and provide insight into the complexity of community-based cellulose degradation.