Genetic factors underpinning phenotypic variation are required if natural selection is to result in adaptive evolution. However, evolutionary and behavioural ecologists typically focus on variation among individuals in their average trait values and seek to characterize genetic contributions to this. As a result, less attention has been paid to if and how genes could contribute towards within-individual variance or trait 'predictability'. In fact, phenotypic 'predictability' can vary among individuals, and emerging evidence from livestock genetics suggests this can be due to genetic factors. Here, we test this empirically using repeated measures of a behavioural stress response trait in a pedigreed population of wild-type guppies. We ask (a) whether individuals differ in behavioural predictability and (b) whether this variation is heritable and so evolvable under selection. Using statistical methodology from the field of quantitative genetics, we find support for both hypotheses and also show evidence of a genetic correlation structure between the behavioural trait mean and individual predictability. We show that investigating sources of variability in trait predictability is statistically tractable and can yield useful biological interpretation. We conclude that, if widespread, genetic variance for 'predictability' will have major implications for the evolutionary causes and consequences of phenotypic variation.