Cut the chicken breasts into large chunks and place them in a skillet with the olive oil over medium heat.
Sprinkle the garlic powder and salt over the chicken, then cook for 6 to 8 minutes, turning once, until the pieces are no longer pink in the center.
Remove the chicken from the skillet and shred it with two forks on a cutting board.
Return the shredded chicken to the skillet and pour in the barbecue sauce. Stir over low heat for 3 to 4 minutes until the sauce coats every piece evenly.
Split the slider buns and place the bottom halves on a serving plate. Spoon the chicken mixture onto each bun.
Sprinkle shredded cheddar cheese over the hot chicken so it melts slightly, then add the top buns.