The Natural Living Center in the Bangor Mall area always has organic meat.
On Saturday mornings, the European Market on Buck Street, across from Bass Park, always has meat of all kinds from Mainely Meats - but they are only open 9-noon. Also eggs, veg, gourmet items, etc.
There's also the winter Orono Farmer's Market, held in the Pine Street Parking lot in downtown Orono from December–April, Second and Fourth Saturdays of the month, 9 am-noon.
Hannaford has a pretty good selection of the Nature's Place chicken. Not organic, but preservative-free, free-range, etc.
And you can always ask local farms.