I would cook the cut up potato in the chicken broth separately, simmering for 15-20 minutes, until the potato is done. I would consider this potato soup, and then use the can of chicken soup to make a sauce for the chicken, and have that as a separate course.

If you mix them together it sounds sort of like you are trying to make clam chowder with chicken instead of clams. While that could work, you might want to look at some clam chowder recipes for ideas. I think I would have added celery to the potatoes to give a more interesting texture and a bit of crunch, plus some onion. I would also have added red pepper, but then I have a lot of that in my yard. Red chili flakes would work also, which I tend to use instead of black pepper.

Lars

I'd probably add cheese... like a sharp cheddar?

I would go in a chicken green chili direction...adding some fresh or frozen roasted green chiles (canned are third rate)...Annaheims/ Big Jims...pureed about half of the potato and left the other half kinda' chunky, sweated some onion....saved the chicken soup for something else...and stirred in some cream/ half n' half/ evaporated milk/ sour cream. Red pepper flakes if the chiles lacked character. Maybe a bit of corn or maybe not.

That is, if I had to use the potato. Rathers would be to save the potato for fresh hash browns with bacon n' eggs.

Freed from having to use the potato, I would make chicken tortilla soup.

Perry, welcome to the Cooking Forum.

I might just make that very simple.

Microwave the potato with skin on.

Cut off some of the potato with the skin and blend with chicken soup till creamy.

Dice cut the potato and simmer in the creamy chicken soup with a little heavy cream. Add a little white wine and pepper.

dcarch

Both potatoes and chicken are very bland unless you add enough seasoning. Since you had broth and a can of chicken soup, just a tad more salt, some pepper, basil, and rosemary. Or tarragon. Seasoning is usually the suspect in a lacking chicken soup.

I would have sauteed some onion, carrot, celery and garlic in butter/olive oil. I would have included thyme, sage and white pepper. Then I would have added the diced chicken to sear it, and deglazed the pan with a bit of white wine, or watered down sherry. I would have topped that off with stock and added the potato, some grated as thickener some in cubes. I would have simmered that with a bay leaf. I would probably throw in a couple of kernels of corn, because the yellow would look pretty.
And it would definitely taste better the 2nd day.
I would not add cheese I might have splashed in some evaporated milk if I wanted a creamier mouth feel.

My Mom always made my Grandmother's Brunswick Stew to welcome the start of winter:

Chicken
Potato
Sliced Carrot
Diced Celery
Frozen Baby Lima Beans, thawed
Canned Whole Kernel Corn, drained
Diced canned tomatoes in juice
Onion (I have to leave this out when I make it now)
A dash of black pepper
Salt to season to your preference
about 1/4 - 1/2 tsp Oregano
Chicken Broth

Cook the chicken in broth until done, debone if not already boneless, and chop into small enough pieces to fit on your spoon. Cook carrot and celery (and onion if using) in a little water until just starting to soften, add potato (and a little more water if needed) and cook until vegetables are close to done; drain. Combine with chicken, broth, and the rest of the ingredients, cook for at least 1/2 hour to get the lima beans soft. I don't have exact measurements because it depends on whether you are cooking for 1 or a crowd. Basically, I use about 1 large potato to 2 chicken breasts and enough of the other veggies to equal about 2 cups mixed (in about equal parts) when I am making it for DH and me for dinner and plan on having the leftovers for lunch.
Edie

I would have roasted the vegetables seasoned with olive oil, salt, pepper. Potatoes, onions, carrots are a good base but you can use cauliflower, parsnips, etc. Added that to chicken stock that had parsley, thyme, and a little dill. Puree' it a bit with immersion blender. I want chunks of potato but a light blend thickens it. Added seasoned, roast chicken, dice or shredded, toward the end. I'd have cooked the veggies and chicken at the same time in my convection oven if I didn't have leftover chicken to use.

I have jars of preserved lemon, so I'd likely add a diced rind for a little extra oomph.

Perry: Welcome to this forum. You will find these cooks will be a mountain of help, so do not hesitate to ask them to ask them any food questions.