Is This 1875 CC Trade Dollar Counterfeit?

It looks genuine (Type 1 Obverse & Reverse)
Problem is that it is rare to see a Morgan with chopmarks and I would
question the authenticity of those especially with them being so heavily punched.
If they aren't genuine, then you have a damaged Morgan.

IMHO, this Trade dollar is genuine. I've three of them in my collection but no CC's. In comparison to many coins, I can see how folks would define them as rare. I personally don't regard them as such.

Out of curiosity, I just searched ebay for "chopmarked Trade dollar." I spotted 46 pieces. In comparison, there are over 230 "rare" 1916-D dimes up for bids, a ratio of 5 to 1. So, if one regards the 1916-D dime as a rare coin, I guess the chopmarked Trade dollars are are even rarer.