Guiding light inside the hollow cores of microstructured optical fibers is a major research field within fiber optics. However, most of current fibers reveal limited spectral operation ranges between the mid-visible and the infrared and rely on complicated microstructures. Here we report on a new type of hollow-core fiber, showing for the first time distinct transmission windows between the deep ultraviolet and the near infrared. The fiber, guiding in a single mode, operates by the central core mode being anti-resonant to adjacent modes, leading to a novel modified tunneling leaky mode. The fiber design is straightforward to implement and reveals beneficial features such as preselecting the lowest loss mode (Gaussian-like or donut-shaped mode). Fibers with such a unique combination of attributes allow accessing the extremely important deep-UV range with Gaussian-like mode quality and may pave the way for new discoveries in biophotonics, multispectral spectroscopy, photo-initiated chemistry or ultrashort pulse delivery.