Add the pecans and chestnuts to a medium saucepan and toast over medium-low heat for 5 minutes, stirring frequently so they don't burn.
Carefully add the water (sauce pan will be hot), then stir in the sugars. Bring the syrup to a boil, then reduce to a simmer. Simmer for 10 minutes, stirring occasionally.
Remove from heat and stir in the vanilla extract. Strain out the nuts (reserve for yogurt or ice cream topping in the fridge).
Allow the syrup to cool at room temperature for 15 minutes, then transfer to a syrup bottle or small container. Store in the fridge for up to 2 weeks!
Notes
**I found steamed and peeled chestnuts in the produce department of my grocery store.