In this paper, we report on a study on gaze behavior by children with Autism Spectrum Disorder (ASD) during a dyadic interaction in a naturalistic environment. Twelve children with ASD were contrasted to twelve typically developing (TD) children, in a semi-structured interaction with a selection of items from the Early Social Communication Scale (ESCS). We used the WearCam, a novel head-mounted eye-tracker designed for children, to obtain gaze information across the broad field of view from the viewpoint of the child. Children with ASD looked downwards more often, and explored their lateral field of view more extensively compared to TD children. We discuss a number of hypotheses in support of these observations.