I passed my water through those cheap water filters and sent it to Ward Industries for a water test.
It came back with 61 PPM of chloride.
In the 3rd edition of the Joy of Homebrewing, Charlie Papazian states:
If you use municipal water that is treated with chlorine, one of the simplest and most dramatic things you can do to improve your beers is to pass all brewing water through a countertop of more elaborate charcoal-type filter to remove chlorine. Chlorine will combine with organic compounds (beer worts included) and produce chlorophenols that even in parts per billion can lend a harsh flavor and aroma to your brew.
So, what level of chloride in my water (PPM) is good enough?