There isn't a built-in grammar checking tool on Chrome, but there are a few extensions that can help you with that. I would recommend either Grammarly or Pro Writing Aid.
Grammarly is a free extension that will scan your writing for grammar mistakes and highlight them for you. You can then click on any mistake to see Grammarly's suggestion for how to fix it.
Pro Writing Aid is a paid extension, but it has a free trial period. It works similarly to Grammarly, but also offers suggestions for improving your writing style.