Impulsivity describes the tendency to act prematurely without appropriate foresight and is symptomatic of a number of neuropsychiatric disorders. Although a number of genes for impulsivity have been identified, no study to date has carried out an unbiased, genome-wide approach to identify genetic markers associated with impulsivity in experimental animals. Herein we report a linkage study of a six-generational pedigree of adult rats phenotyped for one dimension of impulsivity, namely premature responding on the five-choice serial reaction time task, combined with genome wide sequencing and transcriptome analysis to identify candidate genes associated with the expression of the impulsivity trait. Premature responding was found to be heritable (h2 = 13–16%), with significant linkage (LOD 5.2) identified on chromosome 1. Fine mapping of this locus identified a number of polymorphic candidate genes, however only one, beta haemoglobin, was differentially expressed in both the founder strain and F6 generation. These findings provide novel insights into the genetic substrates and putative neurobiological mechanisms of impulsivity with broader translational relevance for impulsivity-related disorders in humans.