The rope trick spell states (emphasis mine):
You touch a length of rope that is up to 60 feet long. One end of the rope then rises into the air until the whole rope hangs perpendicular to the ground. At the upper end of the rope, an invisible entrance opens to an extradimensional space that lasts until the spell ends.
The extradimensional space can be reached by climbing to the top of the rope. [...]
If you cast rope trick near a cliff face, then the rope could use the "ground" as the cliff face and be perpendicular to that, thereby potentially using it as means to cross a chasm. Could this work?