Preheat your grill to 300 degrees. Brush thawed crab legs with olive oil.
In a heavy bottom pot, add the butter over low heat. Allow butter to melt and bring to a simmer. The butter will begin to foam. After 2-3 minutes, or until there appears to be no more foam rising, remove from heat. Using a spoon, skim off all of the foam. For extra perfect clarified butter, run the liquid through cheesecloth.
Add the crab legs to the preheated grill and cook for five minutes. Turn over and cook for another five minutes. Remove from the grill and serve warm with the clarified butter.