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Superconducting gap anisotropy at least an order of magnitude larger than that of the conventional superconductors has been observed in the a-b plane of Bi 2 Sr 2 CaCu 2 O 8+ δ in angle-resolved photoemission spectroscopy. For samples with T c of 88 K, the gap size reaches a maximum of approximately 20 meV along the Cu-O bond direction, and a minimum of much smaller or vanishing magnitude 45 away. The experimental data are discussed within the context of various theoretical models. In particular, a detailed comparison with what is expected from a superconductor with a d x 2-y 2 order parameter is carried out, yielding a consistent picture.