Cucumber and Avocado Soup

1 firm-ripe California avocado
2 English cucumbers (1 1/2 pounds), cut into 1/2-inch pieces
1 (8-ounce, 1 cup) container plain yogurt
3 Tbsp. chopped fresh chives
3 tsp. fresh lime juice
1 tsp. salt, or to taste
1 tsp. chopped fresh jalapeño chile
1 cup small ice cubes
Garnish: diced avocado and chopped chives

Blend everything in the blender and serve with garnish!