Put the oil and popcorn kernels in a Dutch oven or a very large pot and shake to make sure the kernels are coated. Cover the pot with a tight-fitting lid and set over medium heat.
When the popping starts, shake the pot occasionally and turn the pot around on the stove once in a while to avoid having a single hot spot on the bottom.
When the popping slows down to just 1 to 2 pops per second, remove the pot from the stove and pour the popcorn into a large disposable aluminum pan, if using, or two sheet pans. You will have about 20 heaping cups. Discard any unpopped kernels.
Preheat the oven to 200°F.
Combine the brown sugar, butter, corn syrup, and salt in a medium saucepan set over medium heat. Melt the butter and sugar, stirring occasionally, then bring the mixture to a rolling boil.
Let the mixture boil, stirring constantly, until the temperature reaches 250°F on a candy thermometer, about 5 minutes. Remove from the heat and carefully add the baking soda, standing back in case the mixture creates steam. Quickly stir the baking soda into the mixture until it is thoroughly combined.
Quickly pour the caramel over the popcorn (dividing it evenly between the two sheet pans, if necessary) and stir thoroughly to coat the popcorn.
Place the caramel popcorn in the oven and bake it for 15 minutes. Remove the popcorn from the oven and stir it well again to coat more of the kernels. Put the popcorn back in the oven for another 15 minutes, then stir again.
Remove the popcorn from the pan and spread it out in an even layer on two sheets of wax paper. Let the popcorn cool to room temperature, about 30 minutes.
While the popcorn is cooling, melt the chocolate chips in a double boiler (or a large heatproof bowl set over a pot of simmering water) over medium heat, stirring frequently with a rubber spatula.
Use a spoon to drizzle the chocolate slowly and evenly over the popcorn in a thin stream, going back and forth across the layer of caramel corn. The chocolate will not totally cover the popcorn, but try to make sure that every piece has at least a little bit of chocolate on it.
Let the chocolate cool completely for at least 1 hour, then break up the caramel corn into large pieces to store or serve. Store the popcorn in an airtight container for 2 to 3 days.