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: 
I see absolutely no reason why not. It fits perfectly well into "other academic achievements, honors, and activities" (or whatever else your title of this part is). Just don't declare it the biggest achievement in your lifetime and provide the relevant details (conference name, level, session, etc.) in a reasonably full and concise format so that people can appreciate what you are talking about.
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).