Mix cream cheese and sugar in a bowl until smooth. Stir in vanilla extract. Thin filling with a little milk if it appears too thick; it should be the consistency of jelly.
Lay out 1 egg roll on a flat work surface. Add about 2 tablespoons of the cream cheese filling down the middle. Sprinkle a few chocolate chips on top. Brush edges of the wrapper with water. Fold in sides and roll up, pressing in edges to seal. Place seam side-down on a plate. Repeat with remaining wrappers, filling, and chocolate chips.
Heat oil in a deep saucepan over medium heat. Fry egg rolls in batches until golden brown, 1 to 2 minutes per side. Drain on paper towels.