Unfortunately at this time, you cannot show a checklist to only one person.
However, you can assign a checklist to a location using a Location Filter, then you can limit which users can access this location. This essentially allows you to assign a checklist to a specific user. See how to do in the video below:
You can also create an Ad-hoc Task for people from your My Checklists page or your Inbox, which you can see how to do in the video below: