Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation ${Delta}:R{ imes}R{ imes}R{ ightarrow}R$ such that the trace is centralizing on I. Then the trace of ${Delta}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${Delta}$ is nonzero under the same condition, then R is commutative.