Preheat your smoker or grill to 225°F (107°C).
Prepare the filling by mixing cream cheese, cheddar cheese, garlic powder, onion powder, smoked paprika, salt, and black pepper in a bowl.
Slice the jalapeños in half lengthwise and remove seeds and membranes for a milder flavor; fill each half with the cheese mixture.
Lay the chicken breasts flat, and place a stuffed jalapeño half on one side of each breast.
Fold the chicken over the jalapeño so it encloses it completely and secure with toothpicks if necessary.
Brush the outside of the chicken bombs with cooking oil.
Place the chicken bombs in the preheated smoker or on the grill and cook for approximately 2 hours, or until the internal temperature reaches 165°F (74°C).
Remove the bombs from the grill and let them rest for 10 minutes before serving.
Slice the bomb in half to reveal the gooey cheese and jalapeño filling.