  We show that the massive noncommutative U(1) can be embedded in a gauge
theory by using the BFFT Hamiltonian formalism. By virtue of the peculiar
non-Abelian algebraic structure of the noncommutative massive U(1) theory,
several specific identities involving Moyal commutators had to be used in order
to make the embedding possible. This leads to an infinite number of steps in
the iterative process of obtaining first-class constraints. We also shown that
the involutive Hamiltonian can be constructed.
