"Is" is definitely correct - but really, the subject is "two thirds".
"Two thirds" is considered to be a single undivided quantity, not two units out of three. Some measurements are funny like that. Think of a pie chart that has two segments - One is 66.6% and that represents the amount of the forest planted in pine trees.
btw: I notice that sometimes after I post a reply to an unanswered question, a reply by you has appeared while I was off in limbo slowly typing my post.
I do not mean to be duplicating your replies. You are just faster at it than I am. No offence intended.