Tachyon vacuum solution in open string field theory with a constant B field

We show that Schnabl's tachyon vacuum solution is an exact solution of the equation of motion of Witten's open bosonic string field theory in the background of a constant antisymmetric two-form field. The action computed at the vacuum solution is given by the Dirac-Born-Infeld factor multiplied to that without the antisymmetric tensor field.