The electronic band structure and Fermi surface of ZrTe_3 was precisely determined by linearly polarized angle-resolved photoelectron spectroscopy. Several bands and a large part of the Fermi surface are found to be split by 100-200 meV into two parallel dispersions. Band structure calculations reveal that the splitting is due to a change of crystal structure near the surface. The agreement between calculation and experiment is enhanced by including the spin-orbit potential in the calculations, but the spin-orbit energy does not lead to a splitting of the bands. The dispersion of the highly nested small electron pocket that gives rise to the charge density wave is traceable even in the low-temperature gapped state, thus implying that the finite correlation length of the long-wavelength modulation leads to a smearing of the band back-folding.