gifted children ( especially profoundly gifted ones) will act out in anti-social or anti-authoritative means if their academic energies are not allowed to be challenged to their true potential.
We chose not to accelerate our EG ds12 - he'll be going into 7th grade next year. Although many gifted children act out as cawdor mentions when they aren't appropriately challenged in school, not all do. Some do ok, others (like my ds) tend to *act* like things are ok until you find out they've been bottling up a lot of feelings that they just chose to live with for several years rather than tell anyone about.
It's probably impossible for any of us who aren't in your specific school district to give recommendations simply because school districts are all so very different in how they approach gifted education and what they will and won't offer in terms of subject acceleration. For us, the answer that worked best for ds and our HG+ dd8 was to move them to private schools which were purposely a year ahead in curriculum for everyone at the grade they were at, allow for more than one grade level subject acceleration, and that have faculty who actively encourage their students to reach as high as they possibly can in their studies. I've also found it helps to be in private school simply because you're paying tuition and the teachers in turn listen to what you have to say as a parent (we had very frustrating experiences with this in our public schools - for instance, we were told when ds was in early early elementarythat "any child who can print their name can score above the 99th percentile on the WPPSI". (Ironically... our ds who scored that high on the WPPSI.... also couldn't easily write his name due to dysgraphia but... I'm getting lost on a personal rant now!)...
Anyway... for us, the social issue was a concern and I still believe it was the right thing to do, for our ds, to not push for a full-grade acceleration. It's not an issue for many kids, but for some kids it can be - as our ds has gotten older he's also expressed the same feelings to us. His school is still not a great fit (and no school probably ever will be) but he is happy to be with same-age peers and wouldn't want to be in a classroom with older kids.
Best wishes,
polarbear
eta - fwiw, we found middle school has been better overall for our ds than elementary school.
