But wait, you say; it has 5 chords if you include the little turnaround that happens in the middle of a verse and at the start of the guitar solo. You know... "In Birmingham they love the Governor; ooo ooo..." each "ooo" having its own chord, one an F major, the other a C major. And my response; no asshole, if you wanna get technical, it has 4 chords. The F is indeed a newly introduced chord - the C however is also the 2nd chord of the verse (as well as the chorus of course). So suck it, shut down your worthless case, and play Free Bird instead - it serves the same purpose, but also allows you to jerk off on your guitar for 9 straight minutes instead of 3. Do note that despite the solo section having only 3 chords, the actual part that you call a song is a a chordal labyrinth by comparison - you might have to look it up on EZtabs.com, but just do it. Do it for the ladies.
If you really need to crowd-please and your song selection is getting desperately thin, there are even douchier songs that are so douchey that they are easily overlooked. In addition to the aforementioned Free Bird, one might consider Stairway to Heaven, anything by Journey (except Don't Stop Believin because people need to move past the last episode of the Sopranos which made the song relevant again for about a week), or even Werewolves of London, perhaps also Take the Money and Run if you're desperate for a similar 3 chorder. Perhaps a little homework is involved, and perhaps not - if you spent any portion of your childhood listening to classic rock radio, you'll be fine. And if you really just can't pull out some kind of alternative, you probably just kinda suck.
One might also make sure that all other possibilities for the set have been exhausted - oftentimes bands learn tunes to throw into their sets that get omitted for whatever reason. If you have any reservations about playing them, once again look at the alternative and either do your damn homework, or wing it if you have to. Winging shit in front of lots of people is fun. If you're playing for the type of audience that enjoys hearing Sweet Home Alabama, they won't know the difference anyway.
While I am fortunate to have passed the point of playing that song due to my skyrocketing career, you may not be so lucky. Just remember, it doesn't have to be this way. There are so many other options, perhaps right in your own song list. The one buried in your parents' car that was sold 10 years ago.