When individuals are measured more than once in the same context they do not behave in exactly the same way each time. The degree of predictability differs between individuals, with some individuals showing low levels of variation around their behavioural mean while others show high levels of variation. This intra-individual variability in behaviour has received much less attention than between-individual variability in behaviour, and very little is known about the underlying mechanisms that affect this potentially large but understudied component of behavioural variation. In this study, we combine standardized behavioural tests in a chicken intercross to estimate intra-individual behavioural variability with a large-scale genomics analysis to identify genes affecting intra-individual behavioural variability in an avian population. We used a variety of different anxiety-related behavioural phenotypes for this purpose. Our study shows that intra-individual variability in behaviour has a direct genetic basis that is largely unique compared to the genetic architecture for the standard behavioural measures they are based on (at least in the detected quantitative trait locus). We identify six suggestive candidate genes that may underpin differences in intra-individual behavioural variability, with several of these candidates having previously been linked to behaviour and mental health. These findings demonstrate that intra-individual variability in behaviour appears to be a heritable trait in and of itself on which evolution can act.