Hello,
I need to share weekly progress with my dissertation chair. It is extremely time consuming to compile my work each week, then cut and paste all of his suggestions after he returns the Word document.
How can I make this easier on myself? If he buys the software, can he easily leave me feedback within my project? I do not want to write the whole thing in Word - but I afford the back and forth time.
If you’re willing to share the entirety of the project with him, then yes, he could open the project and use inline annotations or comments to leave notes directly in each document. Scrivener doesn’t have the sort of track changes revision tools Word offers, though. He could make edits directly to the text, but you’d either need to use your keen eye to spot the changes or he would need to be sure to add a comment to call it to your attention. I’d suggest taking a snapshot of all your documents before passing the project over, so that you can easily roll back to your last version (perhaps he makes so many changes you hate it, or he accidentally wipes one of your documents without realising it) or could have the snapshot open side-by-side with his annotated copy so you can compare versions.
In addition to the snapshots for version control of the documents within the project, you’ll also absolutely want to ensure you’ve got a full project backup. Since this is your dissertation, I’m going to guess you’ve got an elaborate backup scheme already in place, but you’ll probably want to use File > Back Up > Back Up To… with a date stamp at the end of the week before you let anyone else touch your project. 
If you’re sharing the active version of your project, remember that only one of you could have the project open at a time. If you’re sharing the live project over a network or a sync service like Dropbox, you could still make edits whenever he has it closed; if you’re zipping up your project and passing it over to him until he zips it up and returns it, you’ll be without it for however long that takes.
The other option is to send him a copy of the project at the end of the week–e.g. use File > Back Up > Back Up To… to create the zipped copy and then send it to him–and carry on your own work in different documents of the project. When he gets the annotated version of the project back to you, you could copy and paste the contents of each updated file over its older version in your project. Alternatively you could drag and drop all the updated documents from the annotated project to your copy, but that would import them as new documents into the binder (though retaining their meta-data, notes, etc.), so you’d need to then trash your older versions or otherwise demote them to out-dated status. Any Scrivener links or internal references you had to those documents wouldn’t update to match the new copies.
If you did something like that, I’d suggest using a keyword or label or such to mark the documents that are “checked out” to your advisor, so that you can easily identify which you need to avoid editing while he’s making comments in the other copy. Labels have the advantage of being visible in the binder, but if you’re already using them for something keywords or status could work too.
You might also store your research data in the Scriv Research folder
Which presumably your adviser doesn’t need to see.
And export the draft chapters to Google Docs,
Where others may add comments and revisions
Easily shared, and with no purchase of software.
When all are happy with the final version,
You may export in Word format for final polishing.
MM-
Thank you for the great response. I will need to discuss it with him to see if he is willing to buy and learn the new software (both things are easy enough in my opinion).
Surprisingly, I have not taken the insane precautions I envisioned for my dissertation before this party started 
I have all of my rough data in my dropbox (and in Survey Monkey & the qualitative analysis software I use - Dedoose), and then I have my copy here, which is also saved in my dropbox. I suppose I would curl up and die if something happened to my dropbox. I wonder if I should buy a TimeMachine (I am actually a Mac person). Again - thank you for all of the tips.
ksr
Maybe not a Time Machine, but I’d definitely get some zipped backups on an external drive. Dropbox stores your stuff on the server and whatever other computers you’ve linked, so that’s good, but I’d want a zipped backup of the project too, not just the live copy, just in case something goes wrong to corrupt the project or delete the project or overwrite it all with .wav files of maniacal laughter. Restoring a backup from a zip will be easier than restoring files piecemeal via Dropbox.
Are you using Scrivener on Mac or Windows? If the former, you have another option for collaborating: Sync with External Folder. You can read up on it in section 13.2 of the user manual, but in essence you can choose documents in your projects to automatically sync with another folder, say a Dropbox folder you share with your advisor. Then he can open those RTF files in a regular word processor (Word!) and make comments, etc. and save them back to the shared folder, and you can then sync those back into your project. You can set it up to take snapshots automatically when you sync, and I’d definitely do so in case you don’t like changes he makes or some other accidental overwrite happens. It also would let you compare your version and his edited version side by side.
The big point with this is that although he’d be editing in Word, he’d need to avoid Track Changes–those won’t sync correctly into Scrivener. Regular margin comments will be fine, though; they’ll come in as inspector comments. Coloured text if he makes direct edits will also be preserved.
If you’re on Windows, there’s not an automatic way to sync like this, so although you can manually export to a Dropbox, etc. and then copy changes back into the project, it would be about the same as what you’re already doing with compile.