Wait around 60 days after canceling your Chase credit card account. Then get a copy of all three of your credit reports to make sure the card has been canceled. If it's been canceled, no need to do anything else. If it still shows as active on the reports, then you should contact Chase again and by phone at this time.
However, before you call or send a message to cancel your Chase credit card, you will need to pay off the card balance. To do it fast, you can apply for a balance transfer card. For example, the Discover it® Balance Transfer credit card can be a good option for you. The card gives 18 months of 0% intro APR on balance transfers (a go-to APR applies after that). The balance transfer fee is standard - 3% of the amount transferred. The card has no annual fee and you can keep it after the transferred balance is paid off as the card comes with a cash back rewards program.
If you are cancelling your Chase card because it is too expensive or does not give you rewards you need or simply because you want to apply for a different credit card, look at the best credit cards that are currently offered. If you are after rewards, look at Capital One® Savor® Cash Rewards Credit Card with its big cash bonus and great ongoing rewards on all purchases. If you want to earn miles on all purchases an be able to redeem them for travel or anything you want, look at the Discover it® Miles card.