O ring chains

I have a 520 O ring drive chain fitted which is about 16 years old the bike has only done about 5,000 miles, yesterday I noticed one of the o rings was broken and sticking up from between links. Do the O rings deteriorate due to age and should I think about replacing the chain ASAP or just continue riding it?

Yes with age the O rings will deteriorate and 16 years is very old by modern standards if you consider that a modern bike would replace it's chain every couple of years or so.
The O rings are to keep dirt out of the pin and roller there by decreasing ware and increasing service life. So your chain will ware faster on that pin and other O rings may start to fail if the problem is age related and not due to other reasons such as grit damage to that ring.
I have seen many 100bhp plus bikes with similar problem happily riding about spitting O rings out till normal chain an sprocket ware forced replacement. In many cases the rider was unaware or unconcerned.
It is in my opinion not a problem but i would replace the chain when next convenient opportunity comes along after all this time you have had your money's worth out of it.

16 years is pretty old for an O-ring. I'd ride it and see if the rest of them start breaking. The chain will still fit the sprockets but will wear a bit faster with the O-rings breaking down. I'm trying to think if you would get more life out of the sprockets by replacing the chain now rather than later. Probably would by a little any way.

Yep just use it up till ya can lift the chain out of back sprocket gullyes ~1/3 off depth as thats when I found the teeth wear faster than the chain. If ya ever get the chance to handle a new o-ring & X-ring ya'll see why X-rings cost more yetnsell better to those who handled them both new and well used and why I now refer to the O as Obsolete. I'd rather run a dry plain chain that O ring.

If the rest of the chain is ok you could just take that link out and replace with a correct rivetable link along with the two new "o" rings and little grease packet that comes with them.