Make the mayonnaise: In a small bowl, mix together mayonnaise, garlic, and rosemary and set aside or refridgerate. (You can do this up at least one days in advance if needed.)
In a large bowl, add the ground chicken, 1/2 teaspoon salt, 1/4 teaspoon pepper, and 1/2 of the mayonnaise mixture. Use 2 forks to fold and flod the mixture until well combined. It will be a wet mixture that resembles a batter.
Cut out 4 squares of Glad Press & Seal (or something similar but not saran wrap!) and lay flat. Use a large ice cream scoop to create four portions and scoop one onto each pre-cut square. Create 4 more plastic squares and top each patty. Use a sandwich press or the pottom of a flat pot /pan to gently press chicken misture into 4 perfect patties.
Refridgerate patties 1 - 24 hours.
Preheat a non-stick griddle pan to med-high. Cook burgers for about 5 minutes per side.
Assemble the burgers: Spread a dollop of the remaining mayonnaise mixture on the tops and bottoms of the buns. (Toasted buns are a plus here!) Place the chicken burgers on the bottom halves of the buns. Top each with 1/4 cup of arugula and finish with the top half of the bun.