  We show that interactions result in the emergence of a {\it definite}
relative-phase between two initially incoherent Bose-Einstein condensates. The
many-realization interference fringe visibility is universal at
$g_{12}^{(1)}\sim1/3$ throughout the Josephson interaction regime, as evident
from a semiclassical picture. Other types of incoherent preparation yield
qualitatively different coherence dynamics.
