We present a new Monte Carlo scheme for the efficient simulation of multi-polymer systems. The method permits chains to be inserted into the system using a biased growth technique. The growth proceeds via the use of a retractable feeler, which probes possible pathways ahead of the growing chain. By recoiling from traps and excessively dense regions, the growth process yields high success rates for both chain construction and acceptance. Extensive tests of the method using self-avoiding walks on a cubic lattice show that for long chains and at high densities it is considerably more efficient than configurational bias Monte Carlo, of which it may be considered a generalization.