Washed Down with a Pint of Weissbier
Cili Kaimas probably the place to go for traditional Lithuanian cuisine. It does have a few restaurants in Vilnius (and probably in other cities), so if you're concerned with the "chain" aspect I can understand. I normally am, too, but this place seems to buck many of the traditional chain restaurant problems.
For one, the menu is all traditional Lithuanian food. It doesn't try to pretend by giving you small servings, either. You will leave the place chock full of food. There is also a great ambience. The restaurant I was in was built around a giant tree. Brilliant.
There is also a Nobleman's menu. This is supposedly the gourmet menu (and has the price tag to corroborate that claim). In it you can find hunters' delicacies and other fine dining.
Naturally, I opted for the traditional menu. I'm glad I did, too.