We perform high-coordination three-dimensional (3D) lattice simulations of a single chain of N monomers embedded in matrices of quenched chains, at different concentrations q, using pruned-enriched Rosenbluth sampling. The partition function is well-described by the expression, Z N ðqÞ50:051l N N c21 , where c % 1:16 is a universal constant, and lðqÞ523:39217:36q210:96q 2 is the concentration dependent lattice connectivity constant. For sufficiently long chains, Nտ50, we find that the radius of gyration R varies nonmonotonically with q; R decreases gradually from its unperturbed dimensions R 0 until R=R 0 % 0:9, after which it increases relatively rapidly due to repulsion between monomers. Motivated by the similarity in the shape of the curves, and results on Gaussian chains, we successfully superpose all the simulation data onto a single master curve. Finally, we test the relationship R=R 0 $ ðq c 2qÞ 2d0 , suggested by a Flory-type scaling model, where q c is the critical percolation threshold, and d 0 50:132 is a universal constant.