The question was: A friend of this friend had a friend (did you follow that? wink emoticon ) tell her that she was told by someone at a cancer clinic that baby carrots had chlorine added to make them taste better (and that it made them carcinogenic). Was this true?
The quick answer: NO
The longer answer: First off, you have to realize that there is the telephone game happening here, so the information travelling along the line of people upon repetition is likely to have been changed somehow from it's original form. If this person at a cancer clinic was a worker, then they should be reprimanded if they did indeed give this faulty information.
You'll notice that baby carrots are bright orange and yes they taste better (subjectively to many people). This is because they have been bred to be so. These carrots have been bred to have a higher sugar content, and thus are more attractive to many people's taste buds.
There have been memes in the past suggesting that the white coating that happens to those baby carrots over time, is chlorine coming out. They have called it bleaching. This is simply not the case. That is just from the carrot dehydrating. A baby carrot's entire surface has been cut and exposed. If you took a regular carrot and cut it and put it in the fridge, the same white-blushing would occur on the cut surface.
Baby carrots (along with many other fresh cut ready to eat vegetables) are washed with chlorinated water to reduce contamination from microbes. Excess chlorine is then washed away with potable water and centrifugal drier. According to the Canadian Food Inspection Agency, this is an accepted practice: Section 3.4.1 http://www.inspection.gc.ca/food/fresh-fruits-and-vegetables/food-safety/minimally-processed-ready-to-eat-fruit-and-vegetab/eng/1413673339210/1413673388676?chap=4#s10c4
So baby carrots are perfectly safe to eat, do not have chlorine added to make them taste better and do not cause cancer. If someone is trying to tell you that, then maybe they got their information from a looney quack.