We have exploited the new, deep, near-infrared UltraVISTA imaging of the COSMOS field, in tandem with deep optical and mid-infrared imaging, to conduct a new search for luminous galaxies at redshifts z ~ 7. The unique multi-wavelength dataset provided by VISTA, CFHT, Subaru, HST and Spitzer over a common area of 1 deg^2 has allowed us to select galaxy candidates at z > 6.5 by searching first for Y+J-detected (< 25 AB mag) objects which are undetected in the CFHT+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) ten credible galaxy candidates at z > 6.5 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 SED yields z = 6.98+-0.05 with a stellar mass M* = 5x10^9 Msun, and rest-frame UV spectral slope beta = -2.0+-0.2. The next three are also good candidates for z > 6.5 galaxies, but the possibility that they are low-redshift galaxies or dwarf stars cannot be 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. (2011) in fact all lie 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.
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