Place the peanut butter and honey in a microwave-safe bowl and microwave at 30-second intervals stirring in between until the mixture is smooth and melted. Then, stir in the vanilla. (Alternatively, you can melt this mixture in a small pot on the stove over low heat.)
Pour the Cheerios into a bowl and add the melted peanut butter and honey peanut butter mixture to the bowl.
Press the peanut butter-coated Cheerios mixture into an 8x8 baking pan lined with parchment, patting the top to get things smooth. Refrigerate the bars for 1 hour, then slice into 9 bars and serve.