In underdoped cuprate high-Tc superconductors, various local orders and symmetry-breaking states, in addition to superconductivity, reside in the CuO2 planes. The confinement of the CuO2 planes can therefore play a fundamental role in modifying the hierarchy between the various orders and their intertwining with superconductivity. Here we present the growth of a-axis oriented YBa2Cu3O7-δ films, spanning the whole underdoped side of the phase diagram. In these samples, the CuO2 planes are confined by the film thickness, effectively forming unit-cell-thick nanoribbons. The unidirectional confinement at the nanoscale enhances the in-plane anisotropy of the films. By x-ray diffraction and resistance vs temperature measurements, we have discovered the suppression of the orthorhombic-to-tetragonal transition at low dopings, and a very high anisotropy of the normal state resistance in the b-c plane, the latter being connected to a weak coupling between adjacent CuO2 nanoribbons. These findings show that the samples we have grown represent a novel system, different from the bulk, where future experiments can possibly shed light on the rich and mysterious physics occurring within the CuO2 planes.