One of the most important questions regarding the progenitor systems of Type Ia supernovae (SNe Ia) is whether mergers of two white dwarfs can lead to explosions that reproduce observations of normal events. Here we present a fully three-dimensional simulation of a violent merger of two carbon-oxygen white dwarfs with masses of 0.9 M and 1.1 M combining very high resolution and exact initial conditions. A well-tested combination of codes is used to study the system. We start with the dynamical inspiral phase and follow the subsequent thermonuclear explosion under the plausible assumption that a detonation forms in the process of merging. We then perform detailed nucleosynthesis calculations and radiative transfer simulations to predict synthetic observables from the homologously expanding supernova ejecta. We find that synthetic color light curves of our merger, which produces about 0.62 M of Ni, show good agreement with those observed for normal SNe Ia in all wave bands from U to K. Line velocities in synthetic spectra around maximum light also agree well with observations. We conclude that violent mergers of massive white dwarfs can closely resemble normal SNe Ia. Therefore, depending on the number of such massive systems available these mergers may contribute at least a small fraction to the observed population of normal SNe Ia.