  We have performed a low temperature scanning tunneling microscopy and
spectroscopy study of the iron chalcogenide superconductor FeSe_{0.4}Te_{0.6}
with T_{C}~14 K. Spatially resolved measurements of the superconducting gap
reveal substantial inhomogeneity on a nanometer length scale. Analysis of the
structure of the gap seen in tunneling spectra by comparison with calculated
spectra for different superconducting order parameters (s-wave, d-wave, and
anisotropic s-wave) yields the best agreement for an order parameter with
anisotropic s-wave symmetry with an anisotropy of ~40%. The temperature
dependence of the superconducting gap observed in places with large and small
gap size indicates that it is indeed the superconducting transition temperature
which is inhomogeneous. The temperature dependence of the gap size is
substantially larger than would be expected from BCS theory. An analysis of the
local gap size in relation with the local chemical composition shows almost no
correlation with the local concentration of Se-/Te-atoms at the surface.
