Preheat your oven to 180°C (350°F). Line an 8x8 inch baking pan with parchment paper, leaving some overhang for easy removal.
In a large mixing bowl, combine the peanut butter, honey, and melted butter. Stir with a spatula until the mixture is smooth and creamy, and you can see the ingredients are well incorporated and slightly glossy.
Add the rolled oats and vanilla extract to the wet mixture. Fold everything together until the oats are evenly coated and the mixture is thick but still pliable.
Gently fold in the chocolate chips, distributing them evenly throughout the mixture. The batter will be sticky and slightly chunky with chocolate spots.
Transfer the mixture into the prepared pan and press it down firmly with the spatula or fingers to create an even layer. Make sure to press tightly so the bars hold together well after baking.
Bake in the preheated oven for 15-20 minutes, or until the edges are golden brown and slightly crisp. The center should look moist but not raw, with the chocolate slightly melted.
Remove the pan from the oven and let it cool in the pan for about 10 minutes. The mixture will set slightly as it cools, making it easier to handle.
Transfer the pan to a cooling rack and allow the bars to cool completely, about 20-30 minutes. This helps them firm up and makes slicing easier.
Once cooled, lift the bars out of the pan using the parchment overhang. Slice into squares or rectangles as desired with a sharp knife.
Serve the chewy peanut butter chocolate bars and enjoy their moist, sticky texture with pockets of melted chocolate in every bite.