The recipe for chess pie includes cornmeal and vinegar-why?
The vinegar is there to balance out the amount of sugar.  If you leave it out, it may be sickeningly sweet.  If you don't have vinegar, look up recipes for 'lemon chess pie', which use lemon juice instead.

As for the cornmeal ... it typically thickens the filling, to get it to the proper consistency.  The typical replacement is a bit of flour, but it can leave an off (raw flour) taste if used in significant quantities.