I created,cooked and entered this in a 4th of July grill-off in my town and won first place in the chicken category. I cooked the sauce longer than I wanted (was about 2 seconds from being burnt) but was actually perfect. I put a grilled zucchini round under the mushroom caps to make it "sturdy". My mushrooms wanted to roll over. Bottled key lime juice works great,(Joe and Nelly's brand) but I would not substitute regular lime juice. It just doesn't have the same flavor. Zataran's makes dried shallots.
Mix well, the lime juice and the next 6 ingredients in a bowl. Reserve 1 cup.
Place chicken breasts and marinade in a bowl or marinade container. Marinade at least 30 minutes, turning at least once. (I used large breasts and marinaded overnight, was about 8 hours. I've read since to not marinade chicken this long but it worked for this recipe)
Heat grill to medium (I used Kingsford Brand charcoal but any kind of flavoring chips would add another layer of flavor) Brush a little reserved marinade onto mushrooms. Take chicken straight from marinade to the grill. (discard this marinade!) Grill chicken and mushrooms, turning once, until done. Time depends on the size of the chicken, the mushrooms take about 15 minutes. (You can baste with a little of the reserved marinade if you wish)
Place reserved marinade in a small sauce pan. Cook on medium high heat until sauce starts to thicken to the consistency of honey. (be careful not to burn it) It will turn a dark golden color.
To serve, slice chicken breasts across the grain (short way). Place mushroom cap on plate. Place chicken in/on mushrooms and drizzle sauce over all, or use sauce as a dip. Enjoy. :)