Stars are designed, like upvotes and close votes, in that, they should be used sparingly to determine the worth of questions, or in this case, chat posts.

Whilst in [The 2nd Monitor][1], starwalls and [pointless starring][2] are somewhat commonplace, other chat rooms [don't take so kindly][3] to over starring things.

By limiting stars you can avoid situations [like this][4].

With unlimited stars, you could potentially star everything and then the whole idea of starring to highlight interesting content would become pointless.

  [1]:http://chat.stackexchange.com/rooms/8595/the-2nd-monitor
  [2]:http://meta.codereview.stackexchange.com/a/1629/62429
  [3]:http://chat.stackexchange.com/transcript/message/22139771#22139771
  [4]: https://i.sstatic.net/NIJkm.png