I recovered a chrome HTML file. Can I open it in storyline 360?

You should be able to open an .html file with any web browser, such as Chrome, Firefox, and Safari. However, if that file is programmed to display photos or other media files that you don't have, it won't appear as it was designed to appear.

Storyline files have the .story extension. That's the file type that Storyline will create when you first save a Storyline project. And that's the file type needed to edit and publish a Storyline course.