BaFe2As2 exhibits properties that are characteristic of the parent compounds of the newly discovered iron (Fe)-based high-T(C) superconductors. By combining real-space imaging of scanning tunneling microscopy and spectroscopy (STM+STS) with momentum-space quantitative low-energy electron diffraction (LEED), we have identified the surface plane of cleaved BaFe2As2 crystals as the As terminated Fe-As layer-the plane where superconductivity occurs. LEED and STM+STS data on the BaFe2As2(001) surface indicate an ordered arsenic (As) terminated metallic surface without reconstruction or lattice distortion. It is surprising that STM images the different Fe-As orbitals associated with the orthorhombic structure, but not the As atoms in the surface plane.