This paper presents theoretical results on the instability of a Blasius boundary layer perturbed by Klebanoff modes (i.e. the low-frequency streaks known to be induced by free-stream turbulence). Herein, the Klebanoff distortions are modelled as the signature of a three-dimensional convected gust that may be either isolated or periodic along the spanwise direction. Relatively weak Klebanoff fluctuations can produce $O(1)$ changes tothe near-wall curvature of the base flow profile and, hence, fundamentally alter the nature of its instability characteristics.The perturbed flow is shown to support instabilities that are predominantly inviscid and have significantly larger growth rates and characteristic frequencies than the Tollmien–Schlichting(T–S) modes of an unperturbed Blasius flow. The spanwise mode shape of instabilities in the perturbed flow is determined by theSchrödinger equation, with a potential function that corresponds to the skin friction perturbation due to the Klebanoff distortion. The growth ratesof these modes are determined by the near-wall torsion of the perturbed flow.The unsteadiness of the Klebanoff distortion is shown to be a crucial element in determining the overall instability characteristics.