Spicy Cucumber Avocado Soup

1/2 firm−ripe California avocado
1 1/2 pounds cucumbers, cut into 1/2−inch pieces
1 (8−oz) container plain low−fat yogurt (1 cup)
3 tablespoons chopped fresh chives
1 teaspoon fresh lime juice
1 teaspoon salt, or to taste
1/2 teaspoon chopped fresh jalapeno chile with seeds
1 cup small ice cubes
Garnish: diced avocado and chopped chives

Peel and pit avocado. Blend all ingredients in a blender until very smooth, about 1 minute.