The trend toward more peering between networks is commonly conflated with the trend of Internet flattening, i.e., reduction in the number of intermediary organizations on Internet paths. Indeed, direct peering interconnections bypass layer-3 transit providers and make the Internet flatter. This paper studies an emerging phenomenon that separates the two trends: we present the first systematic study of remote peering, an interconnection where remote networks peer via a layer-2 provider. Our measurements reveal significant presence of remote peering at IXPs (Internet eXchange Points) worldwide. Based on ground truth traffic, we also show that remote peering has a substantial potential to offload transit traffic. Generalizing the empirical results, we analytically derive conditions for economic viability of remote peering versus transit and direct peering. Because remote-peering services are provided on layer 2, our results challenge the traditional reliance on layer-3 topologies in modeling the Internet economic structure. We also discuss broader implications of remote peering for reliability, security, accountability, and other aspects of Internet research.