According to an article in Mental Floss, which gave their recommendations of the 'Best Fried Chicken in all 50 States', the Puritan Backroom in Manchester was tops for New Hampshire.

The Puritan Backroom, which has been around since 1917 and, according to the article, claims to have invented chicken tenders, is one of those restaurants that has a massive following of loyal customers.

Many of those people say the best chicken tenders you will ever taste come from the Puritan Backroom. Not only do they say the chicken is consistently moist but the breading is flavorful and not too heavy. Plus, the choice of how you can order them seems endless. From Buffalo to Regular, Spicy to Coconut. There are rarely any tenders left on the plate to take home.

If you're curious, the article also gives a shout out to these other New England restaurants:

Maine - Figgy's Take Out and Catering in Portland
Massachusetts - Trinia's Starlight Lounge in Somerville
Connecticut - Drumstick Bar B Q in Bridgeport 
Rhode Island - 'North' in Providence
Vermont - Misery Loves Co. in Winooski

Credit Think Stock