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Drought may have been an additional strain but, ttbomk, it hasn't been seen as having enough cause for them to go to such extremes. Cliff dwelling complexes were not isolated. Mesa Verde alone has 600 cliff dwellings contained within the canyons on it, several of which were quite close to other cliff dwellings, with whom they probably shared the same water sources.
I suppose it could depend on the severity of the drought, certainly something caused them to abandon Chaco and then build those extrodinary cliff dwellings and then ashort time later (at most 2 centuries probably less) abandon most of them. This does seem like the behavior of people acting under signifigant strain.
Certainly the collapse of Chaco almost certainly was not a particularily pleasant event and it appears likely that these dwellings were aresponse to the collapse and its aftermath.
Lots of room for speculation.
Pierre