In a large heavy saute pan, cook the chorizo over medium-high heat until crisp, about 6 minutes. Add the onions and cook until translucent, about 4 minutes. Transfer to a paper towel to drain off excess fat.
In a saucepan, add the wine and lemon juice. Bring slowly to a boil and reduce the heat to medium low. Add the cheese and cornstarch and whisk until the cheese is fully melted.
Arrange the tortilla chips on a serving platter. Drizzle with the melted cheese mixture. Top with chorizo-onion mixture. Garnish with the cilantro and chives. Serve immediately.