The recent development in the measurements of spontaneous mental state understanding, employing eye-movements instead of verbal responses, has opened new opportunities for understanding the developmental origin of "mind-reading" impairments frequently described in autism spectrum disorders (ASDs). Our main aim was to characterize the relationship between mental state understanding and the broader autism phenotype, early in childhood. An eye-tracker was used to capture anticipatory looking as a measure of false beliefs attribution in 3-year-old children with a family history of autism (at-risk participants, n 47) and controls (control participants, n 39). Unlike controls, the at-risk group, independent of their clinical outcome (ASD, broader autism phenotype or typically developing), performed at chance. Performance was not related to children's verbal or general IQ, nor was it explained by children "missing out" on crucial information, as shown by an analysis of visual scanning during the task. We conclude that difficulties with using mental state understanding for action prediction may be an endophenotype of autism spectrum disorders.