This note studies the extent to which the type I error of the permutation test based on the log rank score departs from its nominal value in the presence of unequal right censoring. For the asymptotic case, situations are identified that lead to conservative and to nonconservative behaviour, and the amount of conservatism is computed for some specific constant hazard situations. A small Monte Carlo study is used to support the relevance of the asymptotic results in a finite sample setting. That the log rank permutation test is not exact in the presence of unequal right censoring is clearly indicated.