Basic algebraic topology, including homotopy-, chain-, and homology-"groups", for spaces "controlled" over a fixed space Z was set up in SLN, vol 1323, by Anderson and the second author. The "groups" are objects in a certain abelian category associated with the controlled space in question. In this paper we define cochain- and cohomology-"groups" with values in this abelaina category, and we set up Poincaré Duality for manifolds in this context. The relevant orientation class is a (non-controlled) locally finite homology class. The type of control used is inspired by Higson, Pedersen and Roe's "entourages" viewpoint, K-theory, vol. 11.