Preheat the oven to 400 degrees F. Line a rimmed baking sheet with parchment paper.
Drizzle the chicken breasts with olive oil and sprinkle all over with salt and pepper.
Put the chicken on the lined sheet pan skin-side up and roast until an instant-read thermometer reads 165 degrees F, 25 to 30 minutes.
In the meantime, turn the heat to medium-low on a braiser or high-sided skillet with a lid. Add the olive oil and onion and cook, stirring, until slightly softened, about 2 minutes. Add the garlic and let cook until the garlic is fragrant, about 30 seconds to a minute. Add the rice, ranch seasoning and turmeric and stir to coat. Add the chicken broth and 2 cups of water. Increase the heat to medium-high and bring to a brisk simmer. Simmer 2 minutes, then add the cream cheese, lemon juice and one scallion. Stir to incorporate.
Cover the pot and let cook until the rice is tender, 8 to 12 minutes. Remove from the heat, then uncover; fluff the rice, then stir in the peas and carrots. Replace the lid to keep warm until the chicken is done (the residual heat will gently cook the peas and carrots). Remove the chicken from the oven and arrange the chicken on top of the rice skin-side-up.
Sprinkle with the crushed chips and the remaining scallions and serve.