Yes, it is possible! LocalMotive is a venture of the farmer's at Nelsons Farm. There are three different size CSA's (community supported agriculture) available and it's very flexible and reasonably priced. There is a one time $10 membership fee. There are deliveries made to Dover, Durham, Portsmouth, Rye and Exeter on a biweekly basis.
I have ordered my first share and I hope to pick it up on Wednesday. I bought the "family" size share. I'll let you know how it goes.
For more information, check out their website or e-mail them at email@example.com.