Preheat a grill over high heat or start a campfire. Cut four sheets of foil about 12-inches (30cm) long.
Divide the shrimp, sausage, potatoes, and corn between the foil sheets. Drizzle with the chicken broth, then sprinkle with the Cajun seasoning and garlic. Top each packet with a tablespoon of butter.
Fold the foil packets crosswise over the shrimp mixture to completely cover the food. Roll the top and bottom edges to seal them closed.
Place the foil packets on the grill or in the campfire and cook until the shrimp is opaque and the food is hot, 15 to 20 minutes, flipping halfway through.
Carefully open each foil packet and sprinkle with the chives. Serve immediately.