  Let $\mu$ be a matrix-valued measure with the essential spectrum a single
interval and countably many point masses outside of it. Under the assumption
that the absolutely continuous part of $\mu$ satisfies Szego's condition and
the point masses satisfy a Blaschke-type condition, we obtain the asymptotic
behavior of the orthonormal polynomials on and off the support of the measure.
  The result generalizes the scalar analogue of Peherstorfer-Yuditskii and the
matrix-valued result of Aptekarev-Nikishin, which handles only a finite number
of mass points.
