I did the same in my dining area. Scrape, drywall compound filler/ spackle, sand. Repeat until satisfied. Paint.

Otherwise call a professional painter;)

It appears that your walls are textured. After sanding, spackling, and sanding again, you will need to reapply texture to the area Textured paint is available, as is spray on texture. You willl need to experiment to match the existing walls. Good luck..

Thanks so much for your help! I'm on it.

I would get a drywall guy to fill and smooth the walls if this is your home do it right textured walls are just not good.

Just searched cost to smooth out textured walls. It's about $1/square foot. If that's in your budget, it's the best option. In a kitchen, it may entail moving appliances and having no usable kitchen for a while. If you don't hate the texture, I'd just repair the chair rail area and repaint. Everything can be fixed.