Well, the AI really cheats the most on the higher difficulty levels. Therefore, if you have a problem with the AI cheating, you could play on Chieftain or Warlord instead so you don't have to cheat to match the AI.
That was just a suggestion. You do whatever you want; I just dislike cheating a lot. If you want to play on higher levels and cheat, your decision. And if (and I'm not implying anything about you personally, Zouave) you need to cheat on Chieftain to stand a chance, you've come to a great place to learn how to play Civ (unless you don't want to - but then, why would you be here?).