Melt butter in a large stockpot over medium heat. Stir in flour to make a smooth paste and cook for about 3 minutes, stirring constantly. Mix in the onion, celery and garlic; season with salt and pepper. Continue to cook and stir for about 4 minutes.
Gradually whisk in the milk so that no lumps form. Stir in chicken stock and cream. Bring to a simmer, and pour in half of the sherry. Season with dill, Worcestershire sauce and Tabasco sauce. Cover and simmer for about 30 minutes, until soup has reduced by 1/3. Add crabmeat, and simmer for another 10 minutes.
Ladle soup into bowls, and top off with a splash of the remaining sherry and a sprinkle of fresh chives.