Pour 1 1/2 inches of oil into a large heavy pot or high-sided skillet. Clip on a deep-fry thermometer and heat the oil over medium-high heat to 360 degrees F.
Set up a dredging station: Place the flour, eggs, and breadcrumbs in each of 3 separate bowls. Season the breadcrumbs with the paprika, 1 teaspoon salt and a few turns of pepper.
Place a piece of chicken between 2 large pieces of plastic wrap and use a rolling pin or other blunt object to pound the chicken until it is as thin as you can make it without it tearing. Repeat with the remaining chicken.
Coat the chicken first in the flour, then in the egg wash and finally in the breadcrumbs. Fry in batches, flipping once, until golden brown, 2 to 3 minutes. Transfer to a wire rack set over a baking sheet to drain; season both sides with salt and pepper. Hold in a warm oven if not serving immediately. Serve with lemon wedges.