Can't tell without looking at your particular house and how the framing runs. You could potentially run the vent out the back and transition it into the wall between two studs. You can buy that type of venting from the big box stores or elsewhere.

My house isn't framed yet, so I have no limitations yet. The construction supervisor suggested just framing out a chase above the cabinets. He didn't think it would be noticeable.

"He didn't think it would be noticeable."

Really!

He has little concept aesthetics.

In one of your photos, draw 2 vertical lines about 16" apart, imagine them as shadow lines and ask yourself, would I notice this?

1st, what is the recommended CFM for venting of the cooking appliance, by the cooking appliance mfg., which is the design criteria for the venting appliance.

You may find that the volumetric efficiency of a single 3-1/2X10" or 14" rectangular vent may not be sufficient, you may need 2. Which means you would need two chases, or a single wider chase.

In using a chase and to keep a square wall to ceiling intersection or a small profile crown, as pictured, the top plates of the wall are cut out allowing the vent to continue.

An alternative to this is to have the vent exit the wall and continue verticly using opposing 45's which can be concealed behind framing and a wider crown. The important part is that the wall structure remains intact.

You have some homework.

The flue is both shallower and narrower than the vent unit hanging over the stove, especially when it's covered with several more inches of wood frame and trim.

This means, if you wish, your wood frame running to the ceiling can be both shallower and narrower than the lower section. It can be finished with nice carpentry detail and not look heavy at all. A nice gain is that this would give a deeper shelf for display, which can even be run around both sides too.

We did this. I only have about 3-4" shelves on each side, mostly just a detail, but on front the shelf is about 7" deep, which holds just about everything I'd like to display there.

Rosie, do you have picture? I'm not visualizing your solution, but it sounds workable! Thanks.

deleting duplicate

This post was edited by bbstx on Tue, Oct 8, 13 at 13:46

Here is my Paint rendition of what I think the chase/flue will look like with the highlights and shadows. Not great, but I'm really stymied on what to do.

Here is one idea... instead of the dimensions of the chase, they built the wall out wider.

Thanks, deedles. I had also done a Paint version with a wider chase like that but my version wasn't good enough to post. This picture is certainly much better!

I know there is a solution to this problem. I just haven't found exactly what I want yet.

This was my problem, too! I had more than one tortured thread about my hood.
I ended up going through the wall about 2 feet from the ceiling, the ceiling of the adjacent room was lower so it was then easy to go straight up through the attic to the roof. It was much easier than trying to design something that tall to look good in my kitchen.