I have removed the pop-up drain stopper and now have an unobstructed view down into the tailpiece assembly. There are no protrusions or holes in the screw-on chrome top piece by which I could use to prevent it turning when I try to turn the tailpiece from below in order to remove it to install a new one.
In the past when this problem occurred I merely used a small screwdriver to force up the lip far enough in several places in order to grip it with pliers to hold it from turning. In this case, this sink and the vanity-top are all one piece as a molded unit so I'm more afraid of damaging it and then have to replace the whole thing.
I guess my question should have been... is there a special tool for this job...
Thanks for any interest... Corney

What, exactly are you attempting to remove? The assembly itself or the tailpiece that threads into it. If you're trying to remove the pop-up assembly turn out the nut under the drain and if you're trying to unscrew the tailpiece Simply remove the retaining nut that secures that secures the pivot rod and insert a screwdriver in to prevent the assembly from turning. You my now take a pair of pliers and remove the tailpiece. Good luck, Tom

Speedball... thanks for the quick comeback... the tailpiece I'm trying to remove is all one piece. The lower portion slides down into the P.trap,the upper or top end fits up into the underside of the drain hole in the sink It's secured there by a chrome ring which is screwed down into the lower piece from the upper-side. Male thread on this piece to female on lower.(leak-proofing by small bead of silicone or putty around sink drain-hole before screwing this piece down into lower part) Excuse me for seeming to talk down to you Re. Your expertise but others may not be familiar with this application. How do I hold this chrome ring from turning when I try to turn lower unit to separate them.The inside of the ring is completely smooth having no holes or protrusions which could be used to hold it from turning. I'm afraid of damaging the sink if I use a chisel or screwdriver
Is there a special tool? If I wreck the sink I'll need a new wife as well as a sink..

Why are you going through all this hassle when the lavatory pop-ups are so cheap? Let me repeat how I remove a tailpiece.
Simply remove the retaining nut that secures that secures the pivot rod and insert a screwdriver in to prevent the assembly from turning I know of no other way to do it. If you have something special then replace it with a regular pop-up. Good luck, Tom

Thanks form the "not helpful" rating. We're done here!

I have this same problem and I don't understand how this answer helps. So what if you stick a screwdriver in the pivot rod hole. You still can't turn that top sink ring to get it loose.

Directly under the sink is a nut that must be unscrewed. If you don't have the tool in this video a pair of channel locks will work. https://www.youtube.com/watch?v=m0iS557OqmU

Bob,
That is a terrible video.

Randystevens,

Underneath the sink you hold the pop-up assembly and loosen the large nut up next to the sink that holds the gasket and pop-up in place. That is done with a pair of adjustable pliers (also known a Channellocks) Not that ridiculous wrench in the video. You can then push the pop-up assembly up and then remove the sink flange from the top. Sink flanges are chrome or brass so they don't corrode and easy to remove (usually by hand).

PS
You don't stick a screwdriver in the pivot rod hole, you stick a screwdriver inside the sink flange to try to prevent it form turning. Doesn't usually work.