Achievement reads: "Pickup the Chicken within 1 second of a match starting."
Easiest way I found was as followed:
2) Create Room
3) Mode: Chicken Run
4) Map: Only have "Roadside" selected.
5) Max Players: Set to two.
6) Make sure Private Match is checked/enabled by clicking on it.
7) Create Room / Start the Game
8) At the start just run forward and grab the chicken.
9) Listen to the sweet sound of an achievement pop.