This paper addresses the single node broadcast problem over a locally twisted cube (LTQ). The broadcast algorithm proposed for this problem uses a new broadcast tree construction which can run in time O(NlogN) where N=2 n is the number of the nodes in LTQ. The broadcast tree turns out to be optimal in terms of the number of transmission steps. To the best of our knowledge, it is the first time to present an optimal broadcast algorithm for LTQ.