Chicken Stew, the way I make it, is basically chicken noodle soup with more stuff in it and thicker. So sue me. It tastes great, is easy to do and nobody will know that you didn't "stew a chicken" all day long to make it.
Make a slurry with the flour and 1 C of the broth. Put all the other ingredients, except for the more delicate veggies (peas, corn) into a pot and simmer for 15 minutes until the potatoes are barely tender but not falling apart. Add the other vegetables and simmer until tender, about another 5 minutes. Stir in the flour mixture and bring back to a boil. Simmer for 5 minutes until the stew thickens.
If you use dumplings instead of potatoes (both would be greedy) then add the vegetables and the flour slurry after the 15 minute first simmer. Drop the dumplings into the simmering liquid and cover, continuing to cook for 10 minutes or so until the dumplings are floating beautifully and merrily on the surface. Make sure everyone gets a dumpling and spoon the rest of the stew on and around it.