If it's a new chapter, saving it will not publish it (it's two separate steps), meaning you can follow Suin's instructions to view your chapter before you publish it. If the chapter had already been published and you are editing it (making some change or correction, or rewriting it following the reviewers' advice, etc.) once you hit the "SAVE" button it is automatically published and it's visible to everybody. HOWEVER, you are taken immediately to a "view" screen where you can check what has just been published. There you can check whether you're satisfied with the changes.
If you are not, you can hit your browser's backwards button and you'll be back in the editing environment, where you can perform any other correction required before hitting the "save" button again. While it's true your chapter will be visible with "errors" while you check/correct your post, the probability somebody may be reviewing your work exactly in that moment is very low.
Kiss,
Gacela