Combine the olive oil, lemon juice, garlic, oregano, chili powder, salt and pepper in a small bowl. Whisk until well combined.
Place the chicken breasts in a zip-top plastic bag and pound them using a meat mallet or rolling pin until they are an even thickness, about ½-inch thick.
Pour the marinade into the bag with the chicken, seal the bag, and place it in a baking dish (in case of leaks). Turn the bag to coat all parts of the chicken. Place chicken in the refrigerator for 30 minutes to 2 hours.
Clean the grates of a gas or charcoal grill (or use an indoor grill pan). Oil the grill grates and heat the grill to medium high (375-450 degrees F).
Remove the chicken from the marinade and discard extra marinade. Grill chicken for 5-8 minutes per side, until cooked through. The internal temperature of the chicken should reach 165 degrees F. For the best grill marks and juicy chicken, begin cooking the chicken on a hotter part of the grill for a few minutes and then move it to lower heat to finish cooking through.
Let chicken rest for 5 minutes before serving.