Not sure what you mean by a 'single speed' chain. Chains are generally either 3/32 or 1/8 pitch, single speed or not.
The bike would need track ends, not vertical dropouts, in order to be able to do that.
First off I set out to Google "single speed chain" but then I realised you and I both know already that such products exist. I've no idea what makes them vastly different to multispeed chains.
And just about young enough to remember the 10mm Shimano jobbies.
Proof that not even Shimano can alter a global standard that doesn't want to be altered...