Preheat your smoker to 350°F and prepare wood chips or pellets; hickory is recommended but use your preferred smoking wood.
Place the chicken pieces on a large rimmed baking sheet and pat them dry with paper towels.
Rub each piece on all sides with 1 tablespoon olive oil to help the rub adhere.
In a small bowl, combine 1½ teaspoons salt, 1 teaspoon black pepper, 1 teaspoon paprika, ½ teaspoon garlic powder, and ½ teaspoon onion powder.
Sprinkle the spice rub evenly over both sides of all chicken pieces, coating thoroughly.
For boneless breasts and thighs: place the pieces on the smoker, close the lid, and smoke for 10 minutes; flip and smoke another 5–10 minutes more, until the internal temperature reaches 165°F.
For bone-in pieces: place them on the smoker and smoke for 25 minutes, flip, then smoke an additional 20 minutes or until the internal temperature reaches 165°F.
Remove the chicken when it reaches 165°F, let rest briefly, then serve.