In a large bowl, combine ground chicken, chopped onion, minced garlic, breadcrumbs, egg, salt, black pepper, paprika, and dried oregano. Mix until all ingredients are evenly incorporated.
Divide the mixture into 4 equal portions and shape each portion into a patty about 1/2 inch thick.
Heat the olive oil in a large skillet over medium heat.
Cook the chicken patties in the skillet for 6-7 minutes on each side or until the internal temperature reaches 165°F (74°C) and the patties are golden brown.
During the last 2 minutes of cooking, place a slice of cheddar cheese on each patty and cover the skillet to melt the cheese.
Toast the hamburger buns lightly in a separate pan or toaster.
Spread 1 tablespoon of mayonnaise on the bottom half of each bun and 1 teaspoon of mustard on the top half.
Place a lettuce leaf on the bottom bun, then add the chicken patty with melted cheese, followed by a slice of tomato.
Cover with the top bun and serve immediately.