Evolutionary relationships among birds in Neoaves, the clade comprising the vast majority of avian diversity, have vexed systematists due to the ancient, rapid radiation of numerous lineages. We applied a new phylogenomic approach to resolve relationships in Neoaves using target enrichment (sequence capture) and high-throughput sequencing of ultraconserved elements (UCEs) in avian genomes. We collected sequence data from UCE loci for 32 members of Neoaves and one outgroup (chicken) and analyzed data sets that differed in their amount of missing data. An alignment of 1,541 loci that allowed missing data was 87% complete and resulted in a highly resolved phylogeny with broad agreement between the Bayesian and maximum-likelihood (ML) trees. Although results from the 100% complete matrix of 416 UCE loci was similar, the Bayesian and ML trees differed to a greater extent in this analysis, suggesting that increasing from 416 to 1,541 loci led to increased stability and resolution of the tree. Novel results of our study include surprisingly close relationships between phenotypically divergent bird families, such as tropicbirds (Phaethontidae) and the sunbittern (Eurypygidae) as well as between bustards (Otididae) and turacos (Musophagidae). This phylogeny bolsters support for monophyletic waterbird and landbird clades and also strongly supports controversial results from previous studies, including the sister relationship between passerines and parrots and the non-monophyly of raptorial birds in the hawk and falcon families. Although significant challenges remain to fully resolving some of the deep relationships in Neoaves, especially among lineages outside the waterbirds and landbirds, this study suggests that increased data will yield an increasingly resolved avian phylogeny.