We have exploited the new, deep, near-infrared UltraVISTA imaging of the Cosmological Evolution Survey (COSMOS) field, in tandem with deep optical and mid-infrared imaging, to conduct a new search for luminous galaxies at redshifts z ≃ 7. The year-one UltraVISTA data provide contiguous Y, J, H, K s imaging over 1.5deg 2, reaching a 5σ detection limit of Y + J ≃ 25 (AB mag, 2-arcsec-diameter aperture). The central ≃1deg 2 of this imaging coincides with the final deep optical (u*, g, r, i) data provided by the Canada-France-Hawaii Telescope (CFHT) Legacy Survey and new deep Subaru/Suprime-Cam z′-band imaging obtained specifically to enable full exploitation of UltraVISTA. It also lies within the Hubble Space Telescope (HST) I 814 band and Spitzer/Infrared Array Camera imaging obtained as part of the COSMOS survey. We have utilized this unique multiwavelength dataset to select galaxy candidates at redshifts z > 6.5 by searching first for Y + J-detected objects which are undetected in the CFHT and HST optical data. This sample was then refined using a photometric redshift fitting code, enabling the rejection of lower redshift galaxy contaminants and cool galactic M, L, T dwarf stars. The final result of this process is a small sample of (at most) 10 credible galaxy candidates at z > 6.5 (from over 200000 galaxies detected in the year-one UltraVISTA data) which we present in this paper. The first four of these appear to be robust galaxies at z > 6.5, and fitting to their stacked spectral energy distribution yields z phot = 6.98 ± 0.05 with a stellar mass M * ≃ 5 × 10 9M ⊙ and rest-frame ultraviolet (UV) spectral slope β ≃ -2.0 ± 0.2 (where f λ ∝ λ β). The next three are also good candidates for z > 6.5 galaxies, but the possibility that they are dwarf stars cannot be completely excluded. Our final subset of three additional candidates is afflicted not only by potential dwarf star contamination, but also contains objects likely to lie at redshifts just below z = 6.5. We show that the three even-brighter z ≳ 7 galaxy candidates reported in the COSMOS field by Capak et al. are in fact all lower redshift galaxies at z ≃ 1.5-3.5. Consequently the new z ≃ 7 galaxies reported here are the first credible z ≃ 7 Lyman-break galaxies discovered in the COSMOS field and, as the most UV luminous discovered to date at these redshifts, are prime targets for deep follow-up spectroscopy. We explore their physical properties, and briefly consider the implications of their inferred number density for the form of the galaxy luminosity function at z ≃ 7.