Hi @jason ,
There have been several requests for this feature.
As far as I am aware, it is not available yet.
There is a Copy button beneath each message that lets you save an individual message as markdown, but not the whole chat.
For reference, here are links to some of the requests:
A user has posted one possible workaround but, as I am not familiar with the inner workings of the process, I cannot comment on its safety etc:
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