We present sibelius-dark, a constrained realization simulation of the local volume to a distance of 200 Mpc from the Milky Way. sibelius-dark is the first study of the ‘Simulations Beyond The Local Universe’ (sibelius) project, which has the goal of embedding a model Local Group-like system within the correct cosmic environment. The simulation is dark-matter-only, with the galaxy population calculated using the semi-analytic model of galaxy formation, galform. We demonstrate that the large-scale structure that emerges from the sibelius constrained initial conditions matches well the observational data. The inferred galaxy population of sibelius-dark also match well the observational data, both statistically for the whole volume and on an object-by-object basis for the most massive clusters. For example, the K-band number counts across the whole sky, and when divided between the northern and southern Galactic hemispheres, are well reproduced by sibelius-dark. We find that the local volume is somewhat unusual in the wider context of ΛCDM: it contains an abnormally high number of supermassive clusters, as well as an overall large-scale underdensity at the level of ≈5 per cent relative to the cosmic mean. However, whilst rare, the extent of these peculiarities does not significantly challenge the ΛCDM model. sibelius-dark is the most comprehensive constrained realization simulation of the local volume to date, and with this paper we publicly release the halo and galaxy catalogues at z = 0, which we hope will be useful to the wider astronomy community.