Gelfand and Cetlin constructed in the 1950s a canonical basis for a finite-dimensional represen- tation V (�) of U(n, C) by successive decompositions of the representation by a chain of subgroups (4, 5). Guillemin and Sternberg constructed in the 1980s the Gelfand-Cetlin integrable system on the coadjoint or- bits of U(n, C), which is the symplectic geometric version, via geometric quantization, of the Gelfand- Cetlin construction. (Much the same construction works for representations of SO(n, R).) A. Molev (11) in 1999 found a Gelfand-Cetlin-type basis for representations of the symplectic group, using essentially new ideas. An important new role is played by the Yangian Y (2), an infinite-dimensional Hopf algebra, and a subalgebra of Y (2) called the twisted Yangian Y − (2). In this paper we use deformation theory to give the analogous symplectic-geometric results for the case of U(n, H), i.e. we construct a completely integrable system on the coadjoint orbits of U(n, H). We call this the Gelfand-Cetlin-Molev integrable system.