To cook the chicken, heat the oven to 350° F. Arrange the chicken breasts in a baking dish and sprinkle with salt and black pepper. Drizzle each breast with approximately 1 tablespoon olive oil (or more or less, depending on their size.) Cook the chicken until they reach an internal temperature of 165° F, or until the juices run clear when cut into the thickest part. Let the chicken cool, then cut into bite-sized chunks.
If cooking the eggs on the stove, place them in a medium saucepan and cover with about 1" of water. Place over high heat and bring the water to a boil. Once the water reaches a rolling boil, remove from the heat, cover and let sit for 8 minutes (or 7 minutes for slightly jammy eggs). Drain and immediately submerge the eggs in a bowl of ice water until cool enough to handle. Peel and cut into quarters.
Cook the bacon in a large skillet, just until crisp. (Even if you like your bacon SUPER crisp, this salad isn't really the place for that.) Transfer the bacon to a paper towel-lined plate to cool. Chop or crumble into bite-sized pieces.
Add the greens to a large serving bowl. Arrange the greens, chicken, eggs, bacon, red onion and grape tomatoes in rows on top of the greens. Serve the dressing on the side.