Hyatt Gold Passport and American Airlines are offering triple miles for Hyatt stay until January 15th, 2012. You can earn up to 15000 American Airlines miles and thus this promotion is capped at ten stays.
Remember that you need to sign up for the promo and choose American Airline miles instead of points when checking in/out. Quite often these still post as Hyatt Gold Passport points, and either a message to Hyatt Gold Passport customer service through the web or call is required to switch them to miles. 
You can combine this with the current Hyatt Gold Passport promo of extra 5000 points for every three stays that runs until November 15th.
Hyatt Gold Passport Diamond members are also eligible for the Diamond amenity points even when choosing American Airline miles but this requires a call to the customer service. These never post automatically when miles are chosen.
Hyatt also has a similar promo going on with Southwest. For me this promo with American Airlines is better, as I rarely fly Southwest, but do use my American Airlines miles for international business and first class awards on Oneworld partner airlines.
You can register for this offer at: http://www.hyatt.com/gp/en/
Terms and conditions of the offer:
EARN UP TO 15,000 AADVANTAGE MILES WITH HYATT
To be eligible to participate in this Promotion, you must be a member of Hyatt Gold Passport and request enrollment code AA001. Join Hyatt Gold Passport via www.hyatt.com/AAFAL11 or call 1-800-228-3360 and request enrollment code AA001. Receive 1,500 AAdvantage miles per completed eligible stay between October 1, 2011 and January 15, 2012 (“Promotion Period”) at any Hyatt hotel worldwide. A maximum of 15,000 AAdvantage miles may be earned during Promotion Period. You must provide your Hyatt Gold Passport and AAdvantage member numbers at time of check-in, choose miles for your stay and pay an Eligible Rate. Hyatt Gold Passport will track all stays in which your Hyatt Gold Passport and AAdvantage account numbers are provided.
“Eligible Rate” is defined in the Hyatt Gold Passport terms and conditions which can be found here.
All hotel reservations are subject to availability and must be made in advance. Please allow three to four (3 – 4) weeks after checkout for bonus miles to be posted to your Rapid Rewards account (allow 4-6 weeks for bonus miles from stays outside the U.S.). Hyatt Gold Passport reserves the right to alter or withdraw this promotion at any time without notice. This promotion is subject to the complete Terms and Conditions of the Hyatt Gold Passport program. For complete Hyatt Gold Passport program terms and conditions visit goldpassport.com. Hyatt Hotels & Resorts™ encompasses hotels managed, franchised or leased by subsidiaries and affiliates of Hyatt Hotels Corporation. The trademarks Hyatt™, Hyatt Hotels & Resorts™, Park Hyatt™, Andaz™, Grand Hyatt™, Hyatt Regency™, Hyatt Place™, Hyatt Summerfield Suites™, Hyatt Vacation Club™, Hyatt Gold Passport™, and related marks are trademarks of Hyatt Corporation. © 2011 Hyatt Corporation. All rights reserved.
