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If you are cooking this for yourself and not for a group, you can cook the chicken and then add the shrimp after the chicken has cooked for a few minutes. If the chicken is very thin, and you don't specify how thin it is, cook it until the pink is gone. Some chefs won't brown chicken chunks, if adding to a dish like chicken fetachini. Parboiled chicken can be finished in under five minutes. For the shrimp, watch for the color change, also under five minutes. So you will want to stay on watch at the stove while cooking these. Sautee'ing is the way I would do it.
If you are cooking this for a group and are unsure if everyone is able to eat shrimp, keep them separated, from storage to prep to cooking. Some people have a very strong allergic reaction to shellfish.
If kept on ice, in the coldest part of the cooler, the shrimp would be good for about three days, but I'd cook them before that time to get the maximum flavor and quality.
After cooking, about two days, covered in the cooler and they would need to be tossed out.
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- Thank you for the information. I've learned alot about cooking just from reading these answers!