Thank you for subsidizing my credit card, which is not only convenient, but
pays me for that convenience.
Seriously, I hope that $3500 balance is shrinking, not growing. Before we married, my wife ran up some hairy cc balances due to injury and subsequent unemployment. Citi ratejacked her to 30% because of high utilization (10 year customer, perfect payment record).
We BT'd to 0% on BoA and Chase cards, both of which treated her well. That being said, be aware that both of these companies are masters of fine print and fees. Most banks will apply the default rate to your transferred balance for a single late payment. Personally, I loathe carrying credit card balances.
If you are primarily interested in a relatively honest dealer, I would recommend looking at local credit unions for a card. You may not get a 0% BT or a great rewards program, but there is a good chance you will get a low APR, low fees, and a reasonable Agreement and Terms contract.
For a 0% offer, you can look at the Chase Flexible Rewards Card on Chase's site. It will give you 12 months 0% on BT's. After that, you can convert it to a Freedom card, which has better cash-back terms. Just a suggestion...