Spherical coordinate systems, which are ubiquitous in astronomy, cannot be shown without distortion on flat, two-dimensional surfaces. This poses challenges for the two complementary phases of visual exploration—making discoveries in data by looking for relationships, patterns, or anomalies—and publication—where the results of an exploration are made available for scientific scrutiny or communication. This is a long-standing problem, and many practical solutions have been developed. Our allskyVR approach provides a workflow for experimentation with commodity virtual reality head-mounted displays. Using the free, open source s2plot programming library, and the A-Frame WebVR browser-based framework, we provide a straightforward way to visualise all-sky catalogues on a user-centred, virtual celestial sphere. The allskyVR distribution contains both a quickstart option, complete with a gaze-based menu system, and a fully customisable mode for those who need more control of the immersive experience. The software is available for download from https://github.com/cfluke/allskyVR.