Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Peel the butternut squash and cut it into 1/2-inch cubes, then cut the chicken breast into similar bite-sized pieces.
In a large mixing bowl, combine the squash cubes, chicken, olive oil, sea salt, black pepper, rosemary, and thyme.
Toss everything together until the chicken and squash are thoroughly and evenly coated in the oil and herbs.
Spread the mixture in a single layer on the prepared baking sheet, ensuring the pieces are not touching to allow for proper browning.
Roast for 25 to 30 minutes, tossing the ingredients halfway through, until the squash is tender and the chicken is golden and cooked through.
Remove the pan from the oven and immediately add the baby kale and apple cider vinegar to the hot sheet pan.
Toss gently so the residual heat wilts the kale slightly, then transfer to a plate and serve immediately.