In a steamer basket or colander placed over boiling water, steam the lobster tails, covered, for 8 to 10 minutes until the shells are red and the meat is opaque. Allow to cool, then remove the meat and set aside.
In a bowl, mix together the mayo, celery, tarragon, lemon juice, chives, salt and pepper. Fold in the lobster. Slice the buns in half vertically, and broil in an oven for a minute on each side or until toasted. Spread the butter inside, then carefully press your thumbs into the inside of the bread to make more room. Fill the cavity with the lobster mix; garnish with chives.