A high-intensity laser pulse propagating through a medium triggers an ionization front that can accelerate and frequency-upshift the photons of a second pulse. The maximum upshift is ultimately limited by the accelerated photons outpacing the ionization front or the ionizing pulse refracting from the plasma. Here we apply the flying focus-a moving focal point resulting from a chirped laser pulse focused by a chromatic lens-to overcome these limitations. Theory and simulations demonstrate that the ionization front produced by a flying focus can frequency-upshift an ultrashort optical pulse to the extreme ultraviolet over a centimeter of propagation. An analytic model of the upshift predicts that this scheme could be scaled to a novel table-top source of spatially coherent x-rays.A growing number of scientific fields rely critically on high intensity, high-repetition rate sources of extreme ultraviolet (XUV) radiation (wavelengths < 120 nm). These sources provide highresolution imaging for high energy density physics and nanotechnology [1,2], fine-scale material ablation for nanomachining, spectrometry, and photolithography [3][4][5], and ultrafast pump/probe techniques for fundamental studies in atomic and molecular physics [6][7][8]. While XUV sources have historically been challenging to produce, methods including nonlinear frequency mixing [9], high harmonic generation [10,11], and XUV lasing or line emission in metal-vapor and noble-gas plasmas [5,12] have demonstrated promising results. Despite their successes, each of these methods introduces tradeoffs in terms of tunability, spatial coherence, divergence, or efficiency [5,[9][10][11][12]. Photon acceleration offers an alternative method for tunable XUV production that could lessen or even eliminate these tradeoffs.Photon acceleration refers to the frequency upshift of light in response to a refractive index that decreases in time [13,14]. In analogy to charged particle acceleration, the increase in photon energy, i.e. frequency, accompanies an increase in group velocity. In the context of an electromagnetic pulse, the leading phase fronts experience a higher index than adjacent, trailing phase fronts, which manifests as a local phase velocity that increases over the duration of the pulse.The trailing phase front, on account of its higher phase velocity, gradually catches up with the