Understanding the formation and evolution of the first stars and galaxies represents one of the most exciting frontiers in astronomy. Since the universe was filled with neutral hydrogen at early times, the most promising method for observing the epoch of the first stars is using the prominent 21-cm spectral line of the hydrogen atom. Current observational efforts are focused on the reionization era (cosmic age t~500 Myr), with earlier times considered much more challenging. However, the next frontier of even earlier galaxy formation (t~200 Myr) is emerging as a promising observational target. This is made possible by a recently noticed effect of a significant relative velocity between the baryons and dark matter at early times. The velocity difference significantly suppresses star formation. The spatial variation of this suppression enhances large-scale clustering and produces a prominent cosmic web on 100 comoving Mpc scales in the 21-cm intensity distribution. This structure makes it much more feasible for radio astronomers to detect these early stars, and should drive a new focus on this era, which is rich with little-explored astrophysics.