Users shouldn't rep people for what they say in chat.
On the other hand, mods can do so, but only in exceptional circumstances.
If someone does something absolutely amazing in the chat (like teaching a class on how to be a better writer, or stopping a flame war peacefully using social skills) then it is OK for a mod to give them +rep.
Similarly, if someone does something clearly out of bounds (like spamming the chat) then it is OK for a mod to give them -rep.
In either case, the mod should both give a very clear rep reason (preferably quoting the recipient's words), and be prepared for me to contact them manually to check the rep was valid.
The reason I don't want to encourage normal users to do it is that it makes reviewing rep a pain in the ass.
Seriously. How am I supposed to check a 'you said a good thing in chat' rep is justified?
Search for all the lines of chat said by that person... and try to guess which one the rep-giver meant?
That would take too much time.
People should not get away with saying whatever they want in the chat.
I'd love it if we could extend rep to cover the chat.
In terms of making sure rep is legitimate, however... it would be a nightmare.
The potential for abuse is too high, and for this reason, I discourage non-mods from giving rep for what is said in the chat.