Rinse the celery, carrots, and onion under cool water. Chop the celery and carrots into big chunks and quarter the onion. Big pieces hold up well during the long cook and won't turn to mush.
Place your 2 ½ pounds of bone-in chicken pieces right into the crockpot. There is no need to brown them first. Raw chicken gives a lighter, cleaner broth that tastes fresh.
Scatter the celery, carrots, and onion over and around the chicken. Sprinkle the dried basil on top. This layering helps the flavors spread evenly as everything warms up.
Add 6 cups of cold water so the ingredients are mostly covered. Don't fill past the max line on your slow cooker. Keep it simple and avoid stirring, which can cloud the broth.
Cover the pot and set it to Low. Let it cook for 8 to 10 hours, and resist the urge to lift the lid. Your home will start to smell amazing after just a few hours.
Set a fine-mesh strainer over a large bowl and ladle the broth through it. Remove the chicken and bones, then discard the vegetables. They have given all their flavor to the pot.
Let the broth cool slightly, then skim off any fat from the top with a spoon. For an easier job, chill it in the fridge so the fat hardens. Serve it hot or store it for later.