On July 14 2003, Madonna’s Hollywood was released as the second single (excluding Die Another Day, which was released as a single from the soundtrack of the same name) from the American Life album. The song was written and produced by Madonna and Mirwais Ahmadzaï.
Today In Madonna History 
Jay-you got it wrong here! Please make a correction! Hollywood was the third single from American Life-the other four singles from the album were as follows-Die Another Day, title cut, Nothing Fails and Love Profusion-Mercifully for the Remix, the acoustic guitar was taken out!
Thanks Rabbit Bunny! I added a note to clarify since we consider Die Another Day to be a single from the Die Another Day soundtrack, which is the original album on which it was featured at the time of its release.