Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Mix ground chicken, 1/3 cup cilantro, Cheddar cheese, garlic, jalapeno pepper, lime juice, cumin, paprika, salt, and pepper together in a bowl; shape into 4 patties.
Cook patties on grill until the bottom is browned, 3 to 4 minutes; flip the burgers and top with a slice of Cheddar cheese. Continue cooking until no longer pink in the center, 1 to 2 minutes more. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C). Transfer burgers to a plate to rest until juices are reabsorbed into the meat, about 3 minutes.
Put burgers onto split buns and top with guacamole and cilantro.
