I have never heard of anyone hanging chairs on a wall in a formal dining room. Why not find places in your home to put them.

Peter your idea is requiring a bit of creativity , so lets try my idea and see if it could work for you , you will need a whole wall to do this by looking at your chairs, the furniture is formal so lets make the wall formal as well, either get a gallon of jewel tone paint or some elaborate wall paper then get some bicycle hangers not the hooks that are used in garages but fancy ones. Here is a picture of the hangers that I'm talking about .

[houzz=[https://www.houzz.com/photos/west-village-bachelor-pad-eclectic-dining-room-new-york-phvw-vp~17673212[(https://www.houzz.com/photos/west-village-bachelor-pad-eclectic-dining-room-new-york-phvw-vp~17673212)]

Store the chairs, hang some art. Please. The room needs color, and something beside wood. I feel dreary gazing upon it, sorry : ) a rug would be nice too......

IMO you already have too much going on on the walls in the space find a closet and put them in there or remove all the rest of the stuff on that art wall and hang them there with the handers that were mentioned.They actually do this quite often in small spaces in Europe.

Great idea. I agree with Patricia that you should remove or edit the current wall decor before adding the chairs. Can you post additional photos? In the meantime, here are some ideas...