With significantly improved sample quality and instrumental resolution, we clearly identify in the ( pi,0) photoemission spectra from YBa(2)Cu(3)O(6.993), in the superconducting state, the long-sought "peak-dip-hump" structure. This advance allows us to investigate the large a-b anisotropy of the in-plane electronic structure including, in particular, a 50% difference in the magnitude of the superconducting gap that scales with the energy position of the hump feature. This anisotropy, likely induced by the presence of the CuO chains, raises serious questions about attempts to quantitatively explain the YBa(2)Cu(3)O(7-delta) data from various experiments using models based on a perfectly square lattice.