This paper considers the problem of a sender who wishes to favorably influence, through strategic communication of information, the action taken by a receiver. As in the large literature on Bayesian persuasion following Kamenica and Gentzkow [2011] (see also Rayo and Segal [2010] and surveys by Bergemann and Morris [2019] and Kamenica [2019]), we model the sender as committing to a communication strategy and the receiver as best responding to that strategy. A communication strategy for the sender is usually described as a statistical experiment, a function mapping from payoff-relevant states to probability distributions over messages. The key departures from most of the literature and the focus of our analysis are that we enlarge the set of the sender's communication strategies to include ambiguous strategies - strategies for which, from the perspective of both sender and receiver, the probability that a given statistical experiment will be used to generate the signal is subjectively uncertain. Furthermore, the receiver (and possibly the sender as well) is assumed to be ambiguity averse, i.e., averse to this subjective uncertainty about these probabilities. In this paper, we explore whether and to what extent using ambiguous communication can be beneficial for the sender compared to standard, unambiguous communication.