Lightly spray an 8x8-inch pan with cooking spray. Place a piece of parchment paper or wax paper in the pan so that it will cover the bottom and come up two of the sides (this will make it easier to remove the bars from the pan once they set up).
Combine the quick-cooking oats and the crispy rice cereal in a large bowl.
In a small saucepan, combine the butter, honey, light brown sugar, and peanut butter. Heat over medium heat, stirring frequently, until the mixture comes to a boil.
Immediately reduce the heat to low and simmer, stirring constantly, for 2 minutes.
Remove the pan from the heat and stir in the vanilla extract.
Add the peanut butter mixture to the oat mixture; stir until very well combined. You want to make sure that the oats and cereal are evenly coated and there are no dry spots (if you have dry spots, your bars may not hold together well). Work quickly once you start combining everything so that the mixture doesn't get too cool and firm before you put it in the pan.
Transfer the oat mixture to the prepared pan. Press down the mixture very firmly with the back of a spoon or spatula so it is very compact (the more compact it is, the better the bars will hold together).
Immediately sprinkle the chocolate chips evenly over the oat mixture while it is still soft. Gently press them down into the oat mixture with the back of a spoon or spatula so they will adhere to the top of the bars.
Cover the pan and place it in the refrigerator for 1 to 2 hours or until firm.
Remove from the pan; cut into 12 bars or squares.
Wrap each bar individually in plastic wrap. Store in an air-tight container at room temperature or in the refrigerator (they will get very firm in the refrigerator, but they will soften once they warm back up).