The first observation of the B0s→¯D*0ϕ decay is reported, with a significance of more than seven standard deviations, from an analysis of pp collision data corresponding to an integrated luminosity of 3 fb−1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The branching fraction is measured relative to that of the topologically similar decay B0→¯D0π+π− and is found to be B(B0s→¯D*0ϕ)=(3.7±0.5±0.3±0.2)×10−5, where the first uncertainty is statistical, the second systematic, and the third from the branching fraction of the B0→¯D0π+π− decay. The fraction of longitudinal polarization in this decay is measured to be fL=(73±15±4)%. The most precise determination of the branching fraction for the B0s→¯D0ϕ decay is also obtained, B(B0s→¯D0ϕ)=(3.0±0.3±0.2±0.2)×10−5. An upper limit, B(B0→¯D0ϕ)<2.0 (2.3)×10−6 at 90% (95%) confidence level is set. A constraint on the ω−ϕ mixing angle δ is set at |δ|<5.2° (5.5°) at 90% (95%) confidence level.Received 6 July 2018DOI:https://doi.org/10.1103/PhysRevD.98.071103Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.© 2018 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)CP violationPropertiesSymmetriesDiscrete symmetriesCP symmetryCP violationResearch AreasBranching fractionHadronic decaysQuark mixingPhysical SystemsBottom mesonsBottom quarkPropertiesCP violationPolarizationTechniquesHadron collidersParticles & Fields