Early development is characterized by a period of exuberant neural connectivity followed by a retraction and reweighting of connections over the course of development. It has been proposed that this connectivity may facilitate arbitrary sensory experiences in infants that are unlike anything experienced by typical adults but are similar to the sensory experiences of adults with synaesthesia, a rare sensory phenomenon that has been associated with exuberant neural connectivity and that is characterized by strong arbitrary associations between different sensations. We provide the first evidence for this infant-synaesthesia hypothesis by showing that the presence of particular shapes influences color preferences in typical 2- and 3-month-olds, but not in 8-month-olds or adults. These results are consistent with the possibility that exuberant neural connectivity facilitates synaesthetic associations during infancy that are typically eliminated during development, but that a failure of the retraction process leads in rare cases to synaesthesia in adults.