Sharepoint - Files downloading instead of opening in Chrome

This is the way Chrome handles file downloads. Google decided that rather than allowing applications to automatically open files downloaded through Chrome, the files must be downloaded to your local machine. There is, unfortunately, no workaround for this. If you want to automatically open files from Sharepoint to be worked in and saved back up to SP within the browser, you'll need to use a different browser like IE or Firefox.

However, if you simply want the file to download and automatically open the application, see the answer by Tekla. After downloading, you'll click the up arrow / caret (^) next to the download on the status bar, and choose "Always open files of this type". This will cause Chrome to pass the download over to the associated application.