We present the concept and a prototypical implementation of a compact x-ray split-delay system that is capable of performing continuous on-the-fly delay scans over a range of ∼10 ps with sub-100 nanoradian pointing stability. The system consists of four channel-cut silicon crystals, two of which have gradually varying gap sizes from intentional 5 deg asymmetric cuts. The delay adjustment is realized by linear motions of these two monolithic varying-gap channel cuts, where the x-ray beam experiences pairs of anti-parallel reflections, and thus becomes less sensitive in output beam pointing to motion imperfections of the translation stages. The beam splitting is accomplished by polished crystal edges. A high degree of mutual coherence between the two branches at the focus is observed by analyzing small-angle coherent x-ray scattering patterns. We envision a wide range of applications including single-shot x-ray pulse temporal diagnostics, studies of high-intensity x-ray-matter interactions, as well as measurement of dynamics in disordered material systems using split-pulse x-ray photon correlation spectroscopy.