Preheat oven to 350℉ (180℃).
Unroll the pie crust and cover the bottom of a 9-inch deep-dish pie plate. Trim the edge, leaving a ½-inch overhang. Fold the overhang under and lightly press against the rim of the pie plate, then crimp decoratively.
Lightly prick the bottom all over with a fork. Chill until firm, at least 30 minutes (or freeze 10 minutes).
Heat a large skillet or saucepan over medium heat, and add the butter and brown sugar. Quickly stir to combine, then whisk in the corn syrup and salt. Cook until the butter and sugar melt, then remove it from the heat and let it cool slightly.
Beat the eggs and vanilla extract in a medium bowl until foamy without overbeating. Drizzle the egg mixture into the butter and sugar mixture while whisking to thoroughly combine.
Place pecan pieces on the bottom of the pie pan and pour the corn syrup mixture evenly over the pecans. Add chocolate chips. (Decorative chocolate chips and pecan halves can be added about halfway through the baking time if desired.)
Place the pie on a baking sheet to avoid spills, and bake for 50-60 minutes. To prevent edges from browning too quickly, cover the crust with foil or a pie crust shield for about 30 minutes.
Remove from the oven, cool completely before serving (2-4 hours).
Serve pecan pie warm or at room temperature with whipped cream or vanilla ice cream.