We use a large cell Monte Carlo (MC) renormalization procedure to compute the critical exponents of a system of growing linear polymers. We simulate the growth of non-intersecting chains in large MC cells. Dense regions where chains get in each others' way, give rise to connected clusters under coarse graining. At each time step, the fraction of occupied bonds is determined in both the original and the coarse grained configurations, and averaged over many realizations. Our results for the fractal dimension on three-dimensional lattices are consistent with the percolation value. (C) 2002 Elsevier Science B.V. All rights reserved.