Sounds like you want to do a cash-out refinance with credit cards. Most credit cards will let you take out cash advances any time, but not at zero percent interest - you'll pay as much as 24.9 percent APR. Let's take a look at the latest balance transfer offers to see if one might be right for you.
You didn't mention your credit score, but let's start out by assuming it's good to excellent. Unfortunately, you can't transfer the balance to another Chase card, which excludes you from some of their most popular cash back deals.
Keep in mind that you'll typically pay a fee of at least 3 percent of any balance you transfer. So right off the bat, if you're able to transfer your $2,000, you'll actually start off owing $2,060. But at zero percent interest for over a year, I suspect it'll be worth $60 to save a significant chunk of money in interest every month.
And regarding interest, I'd definitely try to find a card that, once the introductory period is over, has a low interest rate. If you're going to carry a balance awhile, and it sounds like you are, a high interest rate could really do a number on your credit. But I'm sure you know that.
It's interesting to note that one of the lowest ongoing interest rate credit cards out there is the credit card that you currently have.
Ironically, if you were switching to the Chase Freedom from another card, you could take advantage of their current introductory balance transfer offer. Pity that credit cards won't occasionally say, "No interest for over a year!" to their current customers. But I guess the day that happens, pigs will be flying in the air.