We want to make Chicken a la King from a recipe I found on Eatingwell.com.
It calls for Dry Sherry to deglaze the pan, but I was wondering if we could sub something non-alcoholic that would be appropriate for this dish.
Not really. Not that will give you the flavor of sherry.
As written you'll lose about 60% of the alcohol during cooking. To lose more, increase the simmer time before adding the flour mixture and after as well.
To minimize further replace the 1 cup of sherry called for with 3/4 cup chicken stock plus 1/4 cup sherry. Increase simmer times as well.
To eliminate any possibility of alcohol and, unfortunately, the sherry flavor
Dry vermouth. I use the Martini and Rossi Extra Dry and it's really cheap - like $3. It's not a super-duper substitute, but it'll do pretty well. Doesn't have the signature taste of sherry, but it's not bad. Really easy on the budget. Also, you can get a little hip flask of gin and have yourself a martini or two with your meal.