Doctor of Credit is reporting a new $300 sign up bonus for opening a Chase Premier Checking account online and setting up direct deposit within 60 days of account opening. This offer should be available nationwide in states that have Chase branches. This offer is best suited to those who do not live near a Chase branch since it can be opened online. There is sometimes a better bonus of $500 total for opening a Total Checking account and a savings account, but that offer is in-branch only (and the most recent one just ended).
Note that the minimum requirements for avoiding the monthly fee are a minimum balance of $15,000 or automatic payments made to your linked Chase mortgage account, but Doctor of Credit reports that may be possible to downgrade to a Total Checking account (with a minimum balance of $1500) after receiving your bonus. This account must be open for at least 6 months to avoid an early termination fee.
This offer is not available for existing Chase checking customers. From the offer terms:
Offer not available to existing Chase checking customers, those with fiduciary accounts, or those whose accounts have been closed within 90 days or closed with a negative balance.
For more terms and details, check out this Doctor of Credit post.