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We introduce a fast implementation of the pivot algorithm for self-avoidingwalks, which we use to obtain large samples of walks on the cubic lattice of upto $33 \times 10^6$ steps. Consequently the critical exponent $\nu$ forthree-dimensional self-avoiding walks is determined to great accuracy; thefinal estimate is $\nu=0.587597(7)$. The method can be adapted to other modelsof polymers with short-range interactions, on the lattice or in the continuum.

Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm