Peel onion and garlic. Chop the onion finely, press the garlic through a garlic press. Cut the avocados in half, remove the stone and peel the halves. Finely dice one half and mix with a tablespoon of lime juice.
Roughly dice the remaining avocados and puree them finely together with the remaining lime juice, 1/4 litre stock, onion and garlic. Stir in the yoghurt and the remaining stock and briefly hold the hand blender in again.
Season to taste with salt and cayenne pepper. Put the soup in a cool place for about 20 minutes. Meanwhile, wash the chilli, cut lengthwise and remove the seeds. Cut the chillies into fine rings. Divide the soup into soup bowls and sprinkle with remaining avocado cubes and, if desired, some chili rings.
Garnish with a slice of lime and serve with tortilla chips.