Dominick's had a relatively brief run in Chicago, at least in the part I grew up in - I don't remember EVER seeing one locally, let alone shopping there, before I moved away circa 1979. At that time the overwhelmingly dominant chain was Jewel, but we did a good part of our shopping at two nearby independent grocers, Sparkle and West Lawn Finer Foods, both near 59th & Pulaski. (I think the latter is still in business.) Jewel effectively killed off competing chains High-Lo and A&P when I was a youngster.
Sparkle had some union problems when the union meatcutters went on strike with no warning. The owner and his son then did the meatcutting, much to the dismay of the union. I remember once it was raining, and the picketing meatcutters took shelter inside the store's entrance vestibule
and refused to leave until the owner called the police. <Bleeping> goons.
Funny anecdote - a friend of mine saw the picket line, and an old man was telling the striking meatcutters how much he supported them. So my buddy walked up and told the old man to ask them what they were making already . . . after a little back and forth, a number came out, and the old man changed his tune - he went on a tirade about the "gorram sumbiches" making too much already and wanting to raise prices for senior citizens on Social Secuity like him.
I vaguely remember shopping at a Kroger
once - but those stores were few and far between back then, and certainly none were nearby.