Once you have earned bonus points or miles (whether they be AA miles, United miles, AmEx points, or whatever) from signing up for a credit card from a credit card company (Chase, CITI, American Express, etc.) the points or miles are yours to keep, however some credit card companies stipulate that you not close the account immediately after earning the points or miles, so I would suggest keeping the credit card account open for at least 10 months (although I believe 6 months is considered by most to be a sufficient amount of time) before closing it.