The concept of competition (with the exception of shotokan aikido I think) is directly contradictory to the idea of harmony in aikido. Shotokan aikido does competition but it is not an Olympic discipline (if by that you mean it is a recognized competition within the Olympic games). The only martial arts I can think of showcased in the Olympics are boxing, wrestling, TKD, Judo and fencing. I'm certain there are others I'm missing (archery and shooting maybe) but aikido is not among them. As aikido is, by its' very nature almost purely defensive it does not lend itself to any competition.
Jeff answered this quite well. I just wanted to add a little.
Shodokan Aikido, AKA Tomiki Aikido, is the only style of Aikido that I know of that has competition. This is also not pure Aikido as Professor Tomiki blended Aikido and Judo.
Perhaps you heard of the Aikido competition in the World Games. Sensei Bruce Bethers of the USJJF/ USMAF told me that the World Games have a demonstration competition for Aikido.