Whether giving a brief description of your research during a networking session at a conference, sharing your science during round table at a speaker lunch, or giving a full length chalk talk for a job interview, you should always be prepared to talk about and present your science effectively without the use of prepared slides or other aids.
Purpose:
As with all presentations, elevator pitches and chalk talks (or any non-slide based talk) are intended to convey succinct pieces of science to the audience in question and convince them of the interest/importance of your research. The key is to be able to judge your audience well and know how to bring them to the level necessary to follow and appreciate your work.
Knowing your audience:
When meeting a speaker over lunch, your audience will be one person, thus it is easy to judge how to compose an effective summary pitch. Look up their website and see what they research - peruse a few of their papers and look for connections between their research and the motivations, methods, or conclusions of your own story. If you think broadly enough, there will always be a connection which you can use to draw your audience in!
This preparation is harder when meeting people during a networking session or during an open chalk talk format. In these situations, it is crucial to know the venue and the typical audience (field of study at a conference, common research thread in a department or company) and pitch to the average person in that audience. You will likely be going slightly over or under the specific expertise of a few people in the room, but you want to aim to be approachable for the most people.
Composition:
Aim for 5-15 minutes (for elevator pitches) and 45 minutes (for full chalk talks). For elevator pitches, every person in the group should be able to fill 15 minutes with engaging content about their scientific motivation/rationale, hypotheses, results, and conclusions. It's much better to run out of time or have to skip things than be staring at your audience in awkward silence.
Be prepared to give a short summary of your work every time you are meeting a speaker or attending a conference.
Provide context/background that starts from the safe zone of your audience (e.g. if you are speaking to a RNA biochemist - perhaps talking about the molecular machinery involved in the mechanism/process you are studying would be appropriate). Be careful not to pander in too overt of a fashion. If there is a large separation between your science and the audience - simply broaden the motivation and scope.
Feel free to use chalk/whiteboard to aid the discussion whenever possible! You can draw figures, schemes, study designs, expected results etc. as you speak to facilitate understanding. View these chalk drawings as figures and supplements to the paper - if the audience looks back at the end and sees the drawings (and maybe some terse phrases), they should be able to remember the full intellectual ark of the presentation.
This is especially crucial for a full chalk talk. Board work (use of pre-drawn starting figures, left to right/up to down movement, and key phrases) is crucial to keeping the audience with you for an entire session and helping them be impressed with your scientific motivation, thought-process, and organization!
Delivery:
Try to make eye contact with your audience when you aren't writing on the chalkboard - use this to gauge whether they are following or if they seem to not understand or believe something. Clarify things on the fly - don't let confusion linger.
Let them interrupt if they wish you a question - some audiences are very interactive but many are not.
Be prepared for aggressive refutation of your statements or your conclusions. This is fairly rare but remaining professional, confident, and assertive when this happens can win you a great deal of respect in the community.
Lastly, have fun doing this! Meeting a speaker or networking at a conference/workshop is a great way to interact scientifically with a wide array of world-class researchers in a relatively low pressure environment. I know of many cases in which confident, clear, and engaging pitches have led to job interviews, postdocs, conference/talk invites, etc!