Technically, neither the Chaparral 2 or the 2C were ever raced in the CanAm series.
The car in Keith's photo ran in the early rounds of the 1965 USRRC championship, and was always just a Chaparral 2, later dubbed "2A" by the press when the actual 2C was built. The 2C was a very different car:

You can see there are no intakes ahead of the rear wheels, and a different tail/wing design. It was all-aluminum instead of having the glass fiber pod that the 2 had.
Both cars were used in 1965, but for the 1966 CanAm, the 2E was ready and was run exclusively by Jim Hall and Phil Hill. As I recall, the 2C was rebuilt into one of the 2Es and some of the regular 2s ended up as 2Ds.
All that said, they certainly were part of the CanAm legacy, in spirit if not in fact.