Remove the sun-dried tomatoes from their jar of olive oil and place them between two layers of paper towels. Gently press the tomatoes to remove any excess oil, then chop them into small pieces. Set the chopped sun-dried tomatoes aside for later use.
Slice the chicken breasts crosswise into thin strips, about ½ inch thick. This helps them to cook quickly and evenly in the skillet.
Heat 1 tablespoon of reserved oil from the sun-dried tomato jar in a large nonstick skillet over medium heat. Once the oil is hot, add the minced garlic and cook, stirring constantly, until fragrant—about 30 seconds. Immediately add the sliced chicken from Step 2, along with the kosher salt, freshly ground black pepper, and dried oregano. Cook the chicken for around 10 minutes, stirring occasionally, until it is cooked through and lightly browned. I like to let the chicken get some color for extra flavor.
Add the chopped sun-dried tomatoes from Step 1 and crumbled feta to the skillet with the cooked chicken. Stir everything together and cook for 1 minute to warm the cheese and tomatoes through. If using arugula, stir it in as well and cook for another minute until it’s just wilted. I like to use arugula here for its peppery bite, but you can skip it if you prefer.
Divide the chicken mixture among plates. Garnish each serving with fresh torn or sliced basil. Serve immediately and enjoy.