I'm not a lawyer, and this is almost certainly misguided advice. But when faced with the same, I requested (and got) in writing that the non-compete clause was nonnegotiable, hoping that, should push come to shove, the clause could be found legally non-binding as a contract of adhesion [1].

Also note that Massachusetts recently (2018) signed into law restrictions on non-competes. One of the major aspects is that such a clause provide "garden leave" pay for employees during their noncompete period. [2]

You can alternatively/also simply ask for more pay in compensation, claiming such a clause is non-standard in the field (personally, I've seen very few), and thus it's a material change to what was previously negotiated. That didn't work for me (I was already at the top of the salary range for the level I was assigned to), but since it doesn't involve lawyers, it's more likely to happen.

[1] https://en.wikipedia.org/wiki/Standard_form_contract#Contrac...

[2] https://www.slnlaw.com/massachusetts-non-compete-act.html