Three days ago I published one for 7500 AA miles. Here is another one for 20,000 miles with basically the same requirements:

This offer was found on Slickdeals and later posts indicate that the $1000 is only an initial deposit and may not have to stay there. Watch your monthly service fees.

To get this offer you should have a Citi AAdvantage Credit Card.

Earn up to 20,000 American Airlines AAdvantage bonus miles from Citibank.
Here’s how:

1. Open and fund a Citibank Regular Checking account in a qualifying account package with $1,000 or more by 7/31/2008.
2. Within 30 days of opening your account, make at least one direct deposit into your account or make at least two electronic bill payments from your account each month for three consecutive months and earn your first 10,000 American Airlines Advantage bonus miles.
3. Continue making a direct deposit into your account or two electronic bill payments from your account each month for the next nine consecutive months and earn an additional 10,000 American Airlines Advantage bonus miles.

PROMOTION DISCLOSURE
Promotion Code: CYAM

When you applied for your Citibank Regular Checking Account, you identified the special offer code of CYAM to receive up to 20,000 American Airlines AAdvantage® bonus miles.
Below are the terms and conditions that you must meet in order to obtain the benefits of this special offer.

Terms and Conditions: •To receive this offer, you must:

1. Open and fund a regular checking account in one of the following qualifying account packages: in the Citibank® Account, (online or by phone) Citibank Everything Counts® Account (by phone) or Citigold® Account (by phone) with $1,000 or more by 7/31/08 using offer code CYAM.
2. Within 30 days of opening your account, make at least one direct deposit into your account or make at least two electronic bill payments from your account each month for three consecutive months to earn your first 10,000 American Airlines AAdvantage® bonus miles.
3. If you qualify for the first 10,000 AAdvantage® bonus miles and continue making a direct deposit into your account or making two electronic bill payments from your account each month for the next nine consecutive months, you will earn an additional 10,000 AAdvantage® bonus miles. Electronic bill payments are those you make using Citibank® Online, Citi MobileSM or CitiPhone Banking®, excluding transfers to linked accounts.

•Each 10,000 American Airlines AAdvantage® bonus miles reward will be credited to your account within 120 days from the end of the statement period in which you met the applicable requirements. Your Citibank regular checking account and Citi® / AAdvantage® credit card account must be in good standing at the time each consecutive 10,000 American Airlines AAdvantage® bonus miles addition is posted to your account.

One offer per Citibank customer. All accounts are subject to approval. Only available for first-time Citibank checking/deposit account customers and is valid only once for any individual.

Offer only available to primary cardmembers on the Citi® / AAdvantage® credit card account. Customer must be a citizen or resident alien of the United States (U.S.) with a valid U.S. taxpayer identification number. Taxes, if any, are customer’s responsibility. Persons under 18 years of age are not eligible. Offer may be modified or withdrawn at any time without notice and is not transferable. Offer expires on 7/31/08.

AmericanAirlines, AAdvantage, AAdvantage and Scissor Eagle Design are registered trademarks of American Airlines, Inc. Your Citi / AAdvantage Card is issued by Citibank (South Dakota), N.A.©2008 2008 Citibank. Citibank, N.A. Member FDIC. Citibank, Citibank with Arc Design, Citiphone Banking, Citibank Everything Counts and Citigold are registered service marks of Citigroup Inc. Citi Mobile is a service mark of Citigroup Inc.