Add widget area to header

I’m a traditional header layout with the navigation underneath the logo. I’ve shrunk the logo size a little to clear up some space to ad an advertisement bar to the right of it.

I want to add a widget area to the header, which template file do I need to edit for my child theme to be able to do this? Normally, it would be header.php, but it isn’t clear that that is the right file.

Can you offer some guidance about where to look?