Don't have my UA off hand, so this is off the top of the head and not positive I'm remembering right...
I think he could be up to level 10 with some rulings of a single class character via the UA who could be multiclass but only utilized one class.
I was looking at mine just today, without the single class bonus and without exceptional strength(18(01) or higher) which drizzt does not have his level limit is 6....thus single class his limit is 8. Hey what can I say, I love 1e still....