Mix all ingredients in a medium sized bowl, add shrimp and toss to coat and refrigerate one hour (or put marinade in a gallon sized plastic bag with shrimp)
Grilling the shrimp
Remove the shrimp from the marinade and pat excess marinade off with paper toweling, discard marinade.
Cook shrimp on a hot grill approximately 2 minutes per side, remove and keep warm
Key Lime beurre blanc
In a small skillet or saucier on medium heat place first five ingredients and reduce liquid to about 3 tablespoons, 4 mins.
Add the cream and reduce to 3 tablespoons, 2 mins.
Take the skillet off the heat and add cold butter 1 tablespoon at a time stirring it in. Place back on the heat a few seconds if it gets too cold to melt the butter. This will help the sauce to not separate.
Remove from heat and strain in a wire sieve.
Put beurre blanc back into the skillet and stir in the key lime zest , salt and chives.
Place in a serving dish and serve right away, using it to top the shrimp.
Notes
Serve shrimp over rice. I cooked the rice in chicken bouillon to give it extra flavor.