There are a lot of free game engines out there. I’m not sure which ones will work with Chromebooks specifically, though. Any recommendations would also depend on the programming language (if any) you want to use.
Codecademy has a course on making games with Phaser, which is a free game framework for making HTML5 browser games. It uses JavaScript so you’d want to be familiar with that before diving too deeply into trying to learn Phaser.