Do you mean chicken on the bone? You don't have this trouble with boneless meat, right?
I think you are probably mistaking connective tissue for blood. Close to the bone, especially in joints, you'll see dark streaks. It isn't blood.
Just use a meat thermometer, and take the chicken out when it is 180 degrees in the thickest part. I usually take it out when it is 170 degrees and let it rest and raise to 180 under tin foil.