Is Grammerly consistent with the Chicago Manual of Style

Though related, grammar and style are two different things. Grammar rules remain the same, regardless of what style manual is being used. If you are writing for a newspaper, you would likely use the AP's style guide. If you are writing for school, it might be APA or MLA. Even Yahoo has its own style guide. We are not employees here, so I don't known what style guides Grammarly's software might use. I suspect that it is a combination of several. I would assume that the grammar checker is not at all a style guide.

To follow up on Patty's answer -- in my experience using the software, Grammarly follows NO style manual. The style manuals tell you how to format a page, what words should be capitalized in cerai situaions, and how to format citatiions and bibliographies. Grammarly does none of those things.

As Patty said, grammar is not style -- Grammarly is a grammar checker and not a style checker.