Add the peanut butter, soy sauce, sweet chili sauce, and brown sugar to a food processor. Puree to blend.
Slowly add water while pulsing the food processor until your desired sauce thickness is achieved. Transfer to a bowl.
Add the soy sauce, 3 tablespoons of peanut sauce, and lime juice. to a small bowl Whisk until smooth.
Place the chicken strips into a gallon-size food storage bag with the marinade. Seal the bag, smush everything around, and then allow to sit for at least 30 minutes.
While the chicken marinates, soak some wooden skewers in water for at least 10 minutes.
Preheat your oven to 350 degrees F.
Add a strip of chicken to each skewer, twisting back and forth so it looks like an "S".
Add the olive oil to a large skillet that can fit the skewers and place over medium heat. Place the chicken skewers in the skillet and cook for 3 minutes on each side or until a deep golden brown color forms.
Place the skewers on a baking sheet and bake for 15 minutes or until the chicken is cooked through.
Remove from the oven and serve warm with the peanut sauce for dipping.