  A deformation of the classical trigonometric BC(n) Sutherland system is
derived via Hamiltonian reduction of the Heisenberg double of SU(2n). We apply
a natural Poisson-Lie analogue of the Kazhdan-Kostant-Sternberg type reduction
of the free particle on SU(2n) that leads to the BC(n) Sutherland system. We
prove that this yields a Liouville integrable Hamiltonian system and construct
a globally valid model of the smooth reduced phase space wherein the commuting
flows are complete. We point out that the reduced system, which contains 3
independent coupling constants besides the deformation parameter, can be
recovered (at least on a dense submanifold) as a singular limit of the standard
5-coupling deformation due to van Diejen. Our findings complement and further
develop those obtained recently by Marshall on the hyperbolic case by reduction
of the Heisenberg double of SU(n,n).
