1. In a food processor, puree avocado with lime juice and lemon juice. Add broth, half-and-half, white pepper, and cumin. Puree until smooth and creamy. Season with salt to taste. Cover and refrigerate until well chilled, about 2 hours.
2. Stir together salsa and chicken. Ladle cold soup into 6 shallow bowls. Top each with about 1/2 cup chicken salsa.