Coherent elastic neutrino-nucleus scattering (CEνNS) offers a unique way to study neutrino properties and to search for new physics beyond the Standard Model. Nuclear reactors are promising sources to explore this process at low energies since they deliver large fluxes of (anti-)neutrinos with typical energies of a few MeV. In this paper, a new-generation experiment to study CEνNS is described. The NUCLEUS experiment will use cryogenic detectors which feature an unprecedentedly low energy threshold and a time response fast enough to be operated in above-ground conditions. Both sensitivity to low-energy nuclear recoils and a high event rate tolerance are stringent requirements to measure CEνNS of reactor antineutrinos. A new experimental site, denoted the Very-Near-Site (VNS), at the Chooz nuclear power plant in France is described. The VNS is located between the two 4.25 GW th reactor cores and matches the requirements of NUCLEUS. First results of on-site measurements of neutron and muon backgrounds, the expected dominant background contributions, are given. In this paper a preliminary experimental setup with dedicated active and passive background reduction techniques is presented. Furthermore, the feasibility to operate the NUCLEUS detectors in coincidence with an active muon-veto at shallow overburden is studied. The paper concludes with a sensitivity study pointing out the promising physics potential of NUCLEUS at the Chooz nuclear power plant. Figure 1: Differential CEνNS count rate on Li 2 WO 4 (solid green line), CaWO 4 (dashed blue line), germanium (dash-dotted red line) and Al 2 O 3 (dotted orange line), calculated with the antineutrino flux expected at the Very-Near-Site from both Chooz-B reactor cores. The reactor neutrino flux model follows [3] as parameterized in [4]. The NUCLEUS experiment aims to reach a background count rate of of 100 counts/(keV·kg·day), indicated by the gray band.