The Massachusetts hunting seasons vary based upon zone as well as upon the animal being hunted. Deer hunting season, for example, generally runs from late September through the end of December. Furbearer season (bobcat, coyote, fox, etc.) can fall anywhere between Jan. 1 to Jan. 31 to Jan. 1 to early March. Check the website for more season date specifics.
Check out these Chesterfield, MA Hunting resources: