Place the onion slices and carrots in the skillet or baking sheet.
Pat the chicken dry with a few paper towels.
Liberally salt the inside of the chicken.
Place the chicken breast side down and drizzle with olive oil in a zigzag motion from top to bottom. Season liberally with salt and pepper. Flip the chicken over and repeat drizzling with oil and seasoning with salt and pepper. Don't forget to season the sides.
You can tie the legs together with twine if you like. Sometimes I do this and sometimes I let them hang loose.
Roast 50 minutes, then check temperature. Temperature should read 165 degrees when an instant read thermometer is inserted into the thickest part of the thigh without touching the bone. See Notes for other methods to check for doneness.
Continue roasting until juices run clear when skin is pierced with a knife, 10 minutes or so longer. Transfer chicken to cutting board. Let stand 10 minutes before carving.
You may notice the carrots look dry on top because they are not stirred while roasting. Simply give it a stir and let them soak up the delicious juices in the pan. Serve vegetables alongside chicken and drizzle pan juices over sliced chicken.
Don't have a thermometer? Here are other ways to check:
Piercing the thigh and checking if juices run clear.
Take out the chicken, cut along the thigh separating it a little from the body, and if the juices run clear, it’s done.
You can also tilt the chicken up and let the juices run out of the cavity. If it's not red, it's okay.