The conformation of linear polymer chains trapped in a matrix of cross-linked polymer has been measured by neutron scattering. Three regimes were found depending on the length of the linear chain, N-l, with respect to the mesh size of the network, N-c. When N-c > N-l, the radius of gyration, R(g), of the linear chain is the same as that observed in the uncross-linked melt. When N-c < N-l, R(g) shrinks according to the scaling relation R(g)(-1) similar to N-c(-1) that has been predicted for isolated polymer chains trapped in a field of random obstacles. When N-c << N-l, the linear chains are observed to segregate.