The authors address propagation of chaos for large systems of rough differential equations associated with random rough differential equations of mean field type \[ dX_t = V(X_t, \mathcal{L}(X_t ))dt + F(X_t ,\mathcal{L}(X_t ))dW_t, \] where \(W\) is a random rough path and \(\mathcal{L}(X_t )\) is the law of \(X_t\). They prove propagation of chaos, and provide also an explicit optimal convergence rate. The first main result shows that, for a sufficiently large class of input signals, propagation of chaos is in fact a consequence of the continuity of the Itô-Lyons solution map for mean field rough differential equations. While the proofs of both the first main result and the underlying continuity property of the Itô-Lyons solution map are mostly based on compactness arguments, the second main result is to elucidate, under slightly stronger assumptions, the convergence rate in the propagation of chaos. The strategy is directly inspired from original Sznitman’s coupling argument for mean field systems driven by Brownian signals. Although the proof is much more involved than in the Brownian setting, the authors recover the same rate of convergence: it coincides with the rate of convergence (in Wasserstein metric) of the empirical measure of an \(n\)-sample of (sufficiently integrable) independent identically distributed variables to their common distribution. In particular, the speed decays with the dimension.