Preheat the oven to 350 degrees F (175 degrees C). Line an 11x17-inch rimmed baking sheet with parchment paper. Spread saltine crackers on baking sheet in a single layer, salted-side up.

Combine butter and brown sugar in a saucepan; melt over medium heat, stirring well until mixture turns a caramel color, about 5 minutes. Pour caramel mixture over crackers and spread evenly.

Bake in the preheated oven until just bubbly, about 5 minutes. Remove from oven and let cool briefly.

Melt chocolate chips in a microwave-safe bowl in the microwave in 15-second intervals, stirring after each melting, 1 to 3 minutes. Pour chocolate over caramel layer and spread evenly.

Transfer baking sheet to the refrigerator and chill until bark hardens, about 1 hour. Break bark up into pieces.