I am not able to save chat log with Telegram. Telegram on Android, Mac OS X, Windows and Linux do not give this option to user, as far as I know. This is a basic feature and it is disappointing and surprising that this software does not have it.
There is a request for this feature here.
Maybe there is a workaround because all history is loaded on the device when you scroll back.
Is it possible to capture/save chat history loaded in the device, make a local backup copy of chat log?