It is very unlikely that CuCl3 exists:
The only two possibble oxidation states of copper are I (cuprous, Cu+) and II (cupric, Cu2+) and if it doesn't exsist then it has also NO name!
For a chem assignment the answer would be no since copper only has +1 and +2 anions
Yes. In fact it is CuCl3-
Also it exists CuCl4=. It occurs in high Cl- concentration solution.