Pour enough vegetable oil in a heavy skillet to cover the bottom about 1/4 inch deep. Heat over medium-high until the oil is hot but not smoking.
Fry for about 1 minute until bubbles form along the edges, then flip it to fry the other side until crisp and lightly browned. Remove the tortilla and drain on paper towels. Repeat with remaining tortillas.
Spread about 2 tablespoons of tomatillo salsa verde on each fried tortilla. Top with shredded chicken, shredded lettuce, and crumbled queso fresco