  In this paper, we give a construction of a (C*-algebraic) quantum Heisenberg
group. This is done by viewing it as the dual quantum group of the specific
non-compact quantum group (A,\Delta) constructed earlier by the author. Our
definition of the quantum Heisenberg group is different from the one considered
earlier by Van Daele. To establish our object of study as a locally compact
quantum group, we also give a discussion on its Haar weight, which is no longer
a trace. In the latter part of the paper, we give some additional discussion on
the duality mentioned above.
