Open pickle jar and transfer pickles to a small bowl using a fork, leaving pickle juice in the jar. Set aside.

In the jar with pickle juice, add brown sugar and 1 teaspoon salt; whisk until dissolved. Add chicken to the jar, making sure all pieces are submerged. Cover and refrigerate for at least 3 hours or up to 12 hours.

Preheat the oven to 400 degrees F (200 degrees C). Line a rimmed baking sheet with aluminum foil.

Remove chicken pieces from pickle juice; discard juice. Thread 1 chicken piece followed by 3 pickle chips onto an 8-inch skewer; repeat layers once, then finish with a third chicken piece. Continue threading remaining chicken and pickles onto skewers as needed; reserve any extra pickles for another use. Place skewers on the prepared baking sheet; pat dry using paper towels. Evenly brush skewers with oil. Sprinkle chicken pieces evenly with ranch dressing mix and remaining ¾ teaspoon salt.

Heat a grill pan over medium-high heat until water sprinkled on immediately sizzles. Grill skewers, pressing down on chicken as needed, just until marks form on two sides, about 1 minute per side. Return skewers to baking sheet.

Bake in the preheated oven until an instant-read thermometer inserted in the thickest part of the chicken registers at least 165 degrees F (74 degrees C), 7 to 12 minutes.

In a small saucepan, melt 2 tablespoons of the butter over medium heat. Add the garlic and cook for 1 minute. Add the chicken broth, 1 tablespoon ranch dressing mix, 2 teaspoons dill, and ⅛ teaspoon salt. Bring to a simmer and cook until slightly thickened, about 2 minutes. Remove from heat and stir in the remaining 2 tablespoons butter until melted and combined.

Serve the chicken skewers drizzled with the sauce and garnished with additional fresh dill.