I am trying to create a CD using the audio from an edited video project. I have exported the audio as an AIFF from Final Cut Pro and it is too large to fit on my CD. Is there a higher quality compression I can use to reduce my file size? This has to be able to be played in any cd player... car, house, computer, etc... I don't want to go MP3 because they sound like crap.

For your creation to play on any cd player, the cda file cannot exceed 74 minutes. 44,100hz 16 bit and dats it. To go beyond that, you will have to release volume 2.

Your aiff being like a wav file will be used for the burn.

Now if you had a wintel machine and could stomach the idea of encoding to wma or mp3 you would then have a myriad of choices available. The bulk of the planet would be able to play it, save for some older generation cd only players.

Sorry Jimmy's right. Making a standard audio CD (AIFF) you are limited to the length of the CD (80min MAX on a 700MB disk).
Of course you don't have to have a Wintel machine to encode it to any other format. The Mac has a million options as well. If you must stick to AIFF for standard CD playback then you're going to have to have a "disk 2" If you don't then you can look at doing an MP3 or Apple's AAC audio, which really does sound great.