Noncommutative Tachyon from Background Independent Open String Field Theory

We analyze the tachyon field in the bosonic open string theory in a constant B-field background using the background independent open string field theory. We show that in the large noncommutativity limit the action of tachyon field is given exactly by the potential term which has the same form as in the case without B-field but the product of tachyon field is taken to be the star product.