Bring a large pot of water (or chicken broth, if using) to a rolling boil. Add the chicken breasts and boil until they are cooked through, which usually takes about 15-20 minutes depending on the thickness of the breasts. There's no need to wait for the water to evaporate; just make sure the chicken is no longer pink inside.
Remove the cooked chicken breasts from the pot and let them cool slightly before handling.
Place the cooled chicken breasts into the bowl of a stand mixer. Use the paddle attachment to shred the chicken finely, about 3-5 minutes on a low to medium setting. If you're doing this by hand, the two-fork method works just fine for pulling the chicken apart into shreds.
To the shredded chicken, add the mayonnaise, finely chopped onion, finely chopped celery, golden raisins, capers, dill (specify fresh or dried based on what was intended), and lemon juice. Mix until all the ingredients are well incorporated. Season the mixture with salt and pepper according to your taste preferences.
Allow the chicken salad to chill in the refrigerator for about one hour to let the flavors meld.
Serve the chilled chicken salad on fresh buns, rolls, or for a lighter option, atop a bed of Boston lettuce leaves.