enameled cast iron can stain easily. you can try warm water & 1T bleach to see if it will dissolve. I assume the stain is where the chicken was in contact with the pot? Depending on the manufacturer, the cast iron underneath the enamel may not have been "raw" meaning it had a coating before the enameling process; if the coating was shellac, it can cause a red/orange/purple result, that may have permeated the pot. also, always use a little liquid or fat if you're going to cook for long periods with enamel.
Before using bleach, just heat some water with a little dish soap in it; then scrub with nylon. If nothing comes up, the bleach may be your last resort. If the bleach doesn't solve it, consider your pot "loved & well used."