DIP: Heat oil in heavy large skillet over medium heat. Add onions and sauté until slightly softened, about 5 minutes. Reduce heat to medium-low and cook until onions are deep brown and begin to crisp slightly, stirring often, about 40 minutes. Add garam masala; stir 1 minute. Transfer to small bowl and cool completely. Mix in crème fraîche. Season to taste with salt and pepper. Cover and refrigerate at least 2 hours. DO AHEAD Can be made 2 days ahead. Keep refrigerated.
PITA CRISPS: Finely chop enough cilantro leaves to measure 2 tablespoons. Chop enough cilantro stems to measure 3 tablespoons. Combine oil and garlic in heavy small saucepan; cook over medium heat until oil begins to bubble around garlic, about 5 minutes. Add chopped cilantro stems. Remove from heat and let steep 10 minutes. Strain oil into small bowl; discard solids in strainer.
PITA CRISPS CONTINUED: Preheat oven to 350°F. Cut each pita bread round horizontally in half. Cut each round into 6 wedges. Place pita wedges on 2 rimmed baking sheets; drizzle with cilantro-garlic oil and toss gently to coat. Arrange pita wedges in single layer; bake 5 minutes. Sprinkle with chopped cilantro leaves and bake until pita wedges are crisp and golden, about 5 minutes longer. Cool. DO AHEAD Can be made 1 day ahead. Store airtight at room temperature.
Sprinkle dip with chives; place on platter. Surround with pita crisps