Preheat your oven to 400°F (200°C). Line a 10x15-inch rimmed baking sheet with parchment paper, leaving some overhang on the sides.
Arrange the saltine crackers in a single, tight layer across the bottom of the prepared pan.
In a medium saucepan, combine the butter and brown sugar. Cook over medium heat, stirring frequently, until the butter is melted and the sugar is dissolved.
Bring the mixture to a rolling boil and cook for 3 minutes, stirring constantly to prevent it from burning.
Remove the pan from the heat and carefully stir in the vanilla extract and salt. The mixture will bubble up.
Immediately pour the hot toffee mixture evenly over the saltine crackers. Use a spatula to spread it to the edges.
Bake for 5 to 6 minutes, until the toffee is bubbly all over.
Remove the pan from the oven and sprinkle the chocolate chips evenly over the hot toffee. Let it stand for 5 minutes to allow the chips to melt.
Use an offset spatula to spread the melted chocolate into a smooth, even layer.
Refrigerate for about 2 hours or freeze for 45 minutes, until the chocolate is completely firm. Break into pieces and serve.