Process first 10 ingredients in a blender or food processor until smooth, stopping to scrape down sides. Cover and chill sauce up to 1 week.
Bring 6 cups water to a boil; add shrimp, and cook 2 to 3 minutes or just until shrimp turn pink. Drain and rinse with cold water. Chill up to 24 hours, if desired.
Peel shrimp, leaving tails on; devein, if desired.
Stir avocado into sauce; spoon sauce evenly into 6 chilled martini glasses or small bowls. Arrange 5 shrimp around edge of each glass; garnish, if desired. Serve with lime-flavored tortilla chips.