We investigated electronic surface states in platinum atom chains grown on Ge(001). Scanning tunneling microscopy/spectroscopy was used to record the electronic landscape on atomic platinum chains. High-resolution spatial maps of individual Pt-dimers near the termini of the chains revealed a difference in the electronic structure between the end dimer region and the chains bulk region. Experiments and tight-binding calculations show a one-dimensional character of the electronic states, decaying rapidly into the chains.