Halve avocados lengthways and remove stones. Using a teaspoon, scoop out avocado flesh, taking care to scrapeaway dark green flesh closest to skin.
Put avocado in a blender or food processor. Add yogurt and one-third of chicken stock and puree until smooth. Stir in remaining stock, lime rind and salt and pepper.
Pour into a bowl, cover and chill for 2 hours. Stir in chives and serve in chilled bowls.