I'm with j on all counts. Lime juice certainly can cook the chicken but it depends on its quantity relative to other ingredients, i.e., the final pH of the mix. We'd really need to see the marinade ingredients and proportions. And what in fact you are marinating - whole chicken? boneless, skinless breasts? Makes a difference.
Zests offer much of the flavor (the oils in the skin have tremendous full flavor) without the acidity. Too, they are fat soluble so work well with oil (if present in the marinade) and with the fat in the chicken. To finesse a marinade use both: zest an entire lime, then add just a bit of the juice to the mix. If you have oil present (or water, wine, stock, etc.) you can usually get away with the mix without fear of cooking, at least with skin-on dark pieces or portions. With breasts only - or if you are marinating for substantial time - go with the zest and a bit less of the juice, then make sure there are other non-acidic liquids present in the mix as well.