In a large bowl, combine ground chicken breast, finely chopped onion, minced garlic, breadcrumbs, egg, salt, black pepper, smoked paprika, and dried oregano. Mix until all ingredients are well incorporated.
Divide the mixture into 4 equal portions and shape each portion into a patty about 3/4 inch thick.
Heat 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 minute 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 mayonnaise on the bottom half of each bun and 1 teaspoon Dijon 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.