Sorry, there is currently no way to automatically assign a user when you import them using the Chrome extension. You will be able to see in the Activity tab of the slideover which person did the import. If you want to get creative, you could create new stages for each person who is doing the importing so that a bulk action assign could be done after the fact. 

Thank you Travis the plug in is a nice feature. adding ability to select assigned to be a nice addition, couple of other suggestions: (1) I don't see an easy way to select the stage. (2) Might be nice to have tag lines pre-populate something along the lines "LinkedIn sourced) to make it easier to filter. 

Argh, you are correct, there is no way to select the stage of the pipeline you're importing into. Ignore my attempt at creativity above. We'll try to get the Assign dropdown integrated some point soon.