Preheat oven to 400 degrees. In a large skillet, heat 1 tablespoon oil over medium. Add onion and cook until softened, about 5 minutes. Add garlic and cook until fragrant, 1 minute. Add artichokes and wine; cook until liquid evaporates, about 8 minutes.
Remove skillet from heat and stir in Neufchatel until blended. Fold in 1 1/4 cups fontina and parsley. Transfer mixture to a 2-quart baking dish; sprinkle with 1 cup fontina. Bake until golden and bubbling, 30 minutes.
Meanwhile, in a large bowl, toss pitas with 1 tablespoon oil; spread on a rimmed baking sheet. Bake until golden and crisp, 15 to 20 minutes. Serve warm dip with pita chips.