I am trying to install a replacement medicine cabinet. The 2x4 frame for the old cabinet is about 1/2" to narrow. Any suggestions on how to fit in the new cabinet without tearing out the drywall and having to replace the drywall.
Thanks.

I see no way that's going to happen.
Need to open it up and do some reframing.

if your only alternative is to reframe and re-drywall then you have nothing to lose by trying this
Cut out the 2 X 4 for the height you need for the new cabinet. then on the far side of the stud, sister a piece of 2 X 4 with an overlap of about 2 or 3 inchs , top and bottom, glue and screw it together . now you should have what is a 2 X 4 stud with a jog in it. . then fit a piece of wood the thickness you need so that the medicine chest fits correctly. then repair the wall , or tear it all out as other posters suggest

It's only a half inch.

Cut out 1/2" of one 2x4. Sure, not the easiest thing to do but easier than opening up the wall. May take a combination of circular saw, sawzall and/or soniccrafter saw plus a chisel but it can be done.

Or, nona's way will work too since it's only one stud.