Question: I currently have on my CV a list of conferences I organized, or co-organized, a list of invited talks, a full list of talks, etc. Recently I have been asked to chair a session in a prestigious conference. I am very honored, and thus wondered: is this something I can feature on my CV? If so, would somewhere along with the conferences organized be "standard"?

Answer: 
Chairing a session during a prestigious conference is certainly a good indication that you are recognised within your community (at least to the conference committee) and they value your contributions to the field. It should be definitely part of your CV (and online CV if you do have one).
These conference chairmanships speak well of your "administrative" ability. Some universities prize this, whether or not they say so. So list at least this one, and possibly others, on your CV.

This don't help your "scholarship" credentials per se. But even scholarship is about networking, and many professors will therefore value you for the contacts you have and the doors that you can open for them.