We use variable-temperature scanning tunneling microscopy (STM) combined with pattern recognition of STM images to demonstrate that the vicinal Ag(115) surface undergoes a true Kosterlitz-Thouless(KT)-type roughening transition. As predicted, the height correlation function remains finite below the roughening temperature and it evolves to a logarithmically diverging function at and above TR. From a quantitative analysis of the height fluctuations we derive a roughening temperature of TR= 465 ± 25 K. Recent diffraction experiments could not confirm a KT-type roughening transition on vicinal surfaces. We attribute this to small residual errors in local surface orientation, which overshadow the real thermally excited height fluctuations.