Yes, I have a US Citizenship but intend to keep my Canadian one secret. Not sure if the US recognizes dual citizenships.
Next time you renew your US passport you'll be asked if you naturalized another citizenship since you last renewed. You'll have to say yes and fill out a form saying that you did it without the intention of losing your US citizenship. Presto. Everybody knows, you've told the truth, and you get to hold both passports.
Even swearing allegiance to the queen and her heirs at the citizenship ceremony doesn't cancel your US citizenship, as long as you're up front about it when you renew your US passport.
And always enter and leave the US with your US passport. It's a pain to carry both, but it's not that bad.
BTW, I'm an expat, and I naturalized about 10 years ago.