  We study Witten's open string field theory in the presence of a constant B
field. We construct the string field theory in the operator formalism and find
that, compared to the ordinary theory with no B field, the vertices in the
resulting theory has an additional factor. The factor makes the zero modes of
strings noncommutative. This is in agreement with the results in the
first-quantized formulation. We also discuss background independence of the
purely cubic action derived from the above string field theory and then find a
redefinition of string fields to remove the additional factor from the vertex.
Furthermore, we briefly discuss the supersymmetric extension of our string
field theory.
