Adding a door frame in a narrow opening is something you could probably do yourself after some reading up on how and/or searching You Tube for "how to" vids.

Add a door frame and door where the "entry" (beside the kitchen) and living room meet, creating an entry separate from the living room, preferably changing out the kitchen door to match or coordinate or compliment it.

You could add a hinged swinging door -- preferably swinging both ways -- with frosted glass:

https://sc01.alicdn.com/kf/HT1zlHEFJJaXXagOFbXW/220761081/HT1zlHEFJJaXXagOFbXW.jpg

You could add a swinging door (like a saloon door in old westerns) or café doors that swing both ways and covering as much or as little of the opening as you choose.

http://0.tqn.com/d/homerenovations/1/S/y/d/-/-/cafe-doors-intro-image.JPG

You could add a two part door (or only the bottom half) with the bottom half as tall as you like:

http://www.isisjoinery.co.uk/images/stable_doors.jpg

@suezbell. Thank you, I will look into that. Never thought of that. I was thinking about something like this.

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Jimmy:

If you don't need a solid door, consider other options:

Vertical blinds can open by separating in the middle or just pulling to one side and they come in bamboo, wood, faux wood, fabric and vinyl:

http://shadesofbeautydecor.com/wp-content/gallery/vertical-blinds/238.jpg

You could create a half closet door with the "framing" being only a single vertical 1"x4" board vertically affixed to only the corner of the kitchen/living room wall where there would surely be a stud behind the dry wall if you use full piano hinges to affix the door(s) to that vertical board and to attach the panels you use to each other along with supporting the bottom of the doors with slides appropriate for the flooring or small castors:

http://door.theblackdrop.com/wp-content/uploads/2016/06/Bifold-Closet-Doors-Lowes.jpg

You could add an overhead rod and add either drapes with a pull tie fixture affixed to the wall on one side or hang a row of vertical beads that you could move aside to walk through.

You could create a sliding barn style door affixed to the wall that separates the kitchen from the living room (likely requiring adding a board at the top of the wall that overhangs the opening in order to have something to which to attach the hardware/rail.

https://www.aosom.com/home-goods/homcom-rustic-6-interior-sliding-barn-door-kit-hardware-set-black-carbon-steel-star.html?utm_source=google_shopping&gclid=CjwKEAjwrcC9BRC2v5rjyvSbhWASJACKkjDzZPbPxRuh6Ri6-Gb30j0mlw-mHiRG-ytiJiGeb88v9xoCS23w_wcB

You could take the barn door idea and create a sliding bookcase.

@suezbell Thank you very much! I will consider these options. You've got lots of creative ideas! :)