  We prove that an $m$ out of $n$ bootstrap procedure for Chatterjee's rank
correlation is consistent whenever asymptotic normality of Chatterjee's rank
correlation can be established. In particular, we prove that $m$ out of $n$
bootstrap works for continuous as well as for discrete data with independent
coordinates; furthermore, simulations indicate that it also performs well for
discrete data with dependent coordinates, and that it outperforms alternative
estimation methods. Consistency of the bootstrap is proved in the Kolmogorov as
well as in the Wasserstein distance.
