It will depend on how it's cut 1 pound of chicken breast (or anything else) will always be 16 ounces.
As for cups, it'll depend on how finely you chop it. A cup of cooked chicken can weigh anywhere from 2 ounces (cut into big cubes) to 5 ounces (finely diced). It will also depend on how much moisture has been cooked out of the chicken.
On average I'd say it's around 3-4 ounces. If you need precision, it's always more accurate to use a scale than a measuring cup for dry items like chicken or flour.
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