Brita Filters and any other water filters can remove part of the Chlorine from the water but Brita Filters or any other filters cannot completely remove all the Chlorine in the Tap water.
Although Brita does claim it will remove Chlorine as well as Copper, lead, Sediment and hardness in the water there's no way for the water filter to remove 100% of the Chlorine.
If you want to fully remove Chlorine from your tap water for drinking or cooking you can boil the Chlorine out of the tap water for 20 minutes and then let it cool down.
The boiling of the tap water will remove 100% of the Chlorine in the water.