  Schramm's Locality Conjecture asserts that the value of the critical
percolation parameter $p_c$ of a graph satisfying $p_c<1$ depends only on its
local structure. In this note, we prove this conjecture in the particular case
of transitive graphs with polynomial growth. Our proof relies on two recent
works about such graphs, namely supercritical sharpness of percolation by the
same authors and a finitary structure theorem by Tessera and Tointon.
