Preheat your oven to 350°F (175°C). Unroll the phyllo dough and cover it with a damp kitchen towel to prevent it from drying out.
Using a pastry brush, spread a thin layer of melted butter on the bottom of your 9x13 inch baking dish.
Place one sheet of phyllo dough in the dish and brush it with melted butter. Repeat this with about 6-8 sheets.
In a mixing bowl, combine the peanut butter and chocolate chips. Spread this mixture evenly over the layered phyllo dough.
Layer another 6-8 sheets of phyllo dough on top of the peanut butter filling, brushing each layer with butter.
Use a sharp knife to cut the baklava into diamond or square shapes.
Bake for about 30-35 minutes, or until the top is golden brown and crispy.
While the baklava is baking, combine the sugar, water, honey, and vanilla in a medium saucepan over medium heat. Stir until dissolved, then bring to a boil and let it simmer for about 10 minutes.
Once the baklava is done baking, remove it from the oven and pour the warm syrup evenly over the top.
Allow the baklava to cool completely in the dish before serving.