Candy cane robber

We have 3 lies and one truth.

The Chef says "The maid did it!". If he is lying, then the Maid didn't steal the cane.

The maid says "I didn't do it!". If she is lying, then she did steal the cane.

Thus, the Chef and the Maid lying at the same time lead us to a contradiction which is "at the same time, the Maid steal and didn't steal". One of them should be telling the truth.

If we pick Maid as the truth teller, she didn't steal. Chef is a liar and then he states that Maid didn't do it. But then Prince says that Chef is lying, but since Prince is a liar, Chef isn't lying, which again lead us to a contradiction.

So the only choice left to us is pick Chef as the truth teller and get the conclusion that Maid stole the candy cane.

If the Butler is the one telling the truth, then the maid and the prince must both also be telling the truth.

If the Prince is telling the truth, then the maid must also be telling the truth.

If the maid is telling the truth, the prince must also be telling the truth.

All of these result in multiple people telling the truth, leaving the only person who can be telling the truth as the Chef, because him telling the truth results in the Butler lying about having done it, the Prince lying about the Chef lying and the maid lying about having not done it.

The chef and the maid cannot both be lying; they would contradict each other. Therefore, one of them is telling the truth. From there, you need to simply check both to show that the chef is telling the truth, and the maid stole the cookie.

The chef and the maid are being contradictory, so one lies and the other is being honest. We're told that only one among them is telling the truth, then both the butler and the prince must be lying together and one of them implied in their lies that the chef is actually being truthful. "The maid did it", as the chef honestly says.