We have studied the frustrated system YBaCo4O7.0 generally described as an alternating stacking of kagome and triangular layers of magnetic ions on a trigonal lattice, by single-crystal neutron diffraction experiments above the Néel ordering transition. Experimental data reveal pronounced magnetic diffuse scattering, which is successfully modeled by direct Monte Carlo simulations. Long-range magnetic correlations are found along the c axis, due to the presence of corner-sharing bipyramids, creating quasi-one-dimensional order at finite temperature. In contrast, in the kagome layers (ab plane), the spin-spin correlation function, displaying a short-range 120 degrees configuration, decays rapidly as typically found in spin liquids. YBaCo4O7 experimentally realizes a new class of two-dimensional frustrated systems where the strong out-of-plane coupling does not lift the in-plane degeneracy, but instead acts as an external "field."