Heat the oil in a saucepan over medium-high heat until warm and shimmering. Add the onion and cook until softened, 3 to 4 minutes. Add garlic and cook for 1 minute. Add the ketchup and water and bring to a boil, stirring frequently. Reduce the heat to medium-low and simmer for 5 minutes.

Add the mustard, vinegar, Worcestershire sauce, chipotle chile, ancho chile powder, paprika, brown sugar, honey, and molasses to the pan and bring to a simmer. Cook, stirring occasionally, until thickened, about 10 minutes. Let cool for at least 10 minutes.

Scrape the barbecue sauce into a food processor or blender and purée until either smooth or the desired consistency. The sauce will be quite, quite thick. Let cool to room temperature. Taste and season with salt and pepper accordingly. You can start using it right away, but if you wait overnight the flavor is a little better. (You can cover and refrigerate the sauce for up to 1 week. Bring to room temperature before using.)

Marinate the chicken in this sauce for at least one hour in the fridge. Cook the chicken on the grill or skillet until done and then give it another brush of the sauce before serving.