  We study the superconducting(SC)-gap anisotropy of the \Gamma-centered hole
Fermi surface in optimally doped FeTe_{0.6}Se_{0.4} (T_c = 14.5 K), using
laser-excited angle-resolved photoemission spectroscopy (ARPES). We observe
sharp superconducting coherence peaks at T = 2.5 K. In contrast to earlier
ARPES studies but consistent with thermodynamic results, the momentum
dependence shows a \cos(4\varphi) modulation of the SC-gap anisotropy. The
observed SC-gap anisotropy strongly indicates that the pairing interaction is
not a conventional phonon-mediated isotropic one. Instead, the results suggest
the importance of second-nearest-neighbor electronic interactions between the
iron sites in the framework of s_\pm-wave superconductivity.
