We calculate the joint probability distribution for end–to–end and binormal vectors for a random walk of chiral steps, firstly by a simple combinatoric lattice model, and then fully by Raleigh's method of random flights. We illustrate in the lattice picture that, for quenched end–to–end vectors, an application of shears causes a chiral bias. Armed with this underlying geometrical mechanism, we construct the extension of the classical theory of rubber elasticity for a nematic network of chiral chains. We derive the fully nonlinear piezoelectric response. The small–strain limit gives the linear piezoelectric coefficients for the network. The results are of the universal form mostly encountered in rubber elasticity theory, being proportional to the crosslink density, the chiral strength of a monomer and to a geometrical combination of deformation and nematic tensors.