Take the chicken breasts out of the fridge and let them come to room temperature. Preheat the oven to 375°F (190°C). Spray an 8" x 11" (or similar-sized) baking dish with non-stick spray.
Drain the 6 oz can of black olives. Chop the black olives, chop the 1/4 cup green olives, chop the 1/4 cup capers, and chop the 2 T red onion.
In a bowl, combine the chopped black olives, chopped green olives, chopped capers, chopped red onion, 1 tsp minced garlic, 2 T Dijon mustard, 2 T fresh lemon juice, and 2 T olive oil. Stir to make the topping. (Reserve the remaining 1 T olive oil for browning the chicken.)
Trim the chicken breasts as needed. Evenly sprinkle the 2 tsp Poultry Seasoning over all the breasts, then add salt and fresh-ground black pepper to taste.
Heat the reserved 1 T olive oil in a large frying pan over medium-high heat. When the oil is hot, add the chicken breasts and brown about 5 minutes per side, until nicely browned (they will not be fully cooked).
Remove the browned breasts to a cutting board. Cut each breast lengthwise into 3 or 4 strips (use 4 strips for larger breasts or 3 for smaller ones), keeping the strips about the same thickness for even cooking.
Arrange the chicken strips in the prepared baking dish in a single layer. Spoon the olive-and-caper topping evenly over the chicken so the pieces are well covered.
Bake in the preheated oven for 20–25 minutes, until the chicken is cooked through and the dish is bubbling hot. The internal temperature should reach 165°F (75°C); use an instant-read thermometer if you have one and cook a few minutes longer if needed.
Serve the chicken hot, spooning the sauce and pan juices over the strips.