Explain "while on a chain" Does that mean you are just hooking her up in your back yard, and she won't pee? Will she pee when you take her for a walk?

I gather you were walking her and she wouldn't go. My suggestion was to put her on a very long tie out so she doesn't feel restricted. Just ensure the collar is tight enough so she can't slip out of it. Then leave her by herself, but look at her from a window. When she does it, rush out and give her lots of praise and her favorite treat.

I had one of my dog's so yard potty trained that he wouldn't pee outside while on walks. He finally followed the other dog's lead and began peeing while on walks. Still to this day he will not do the other while on walks. Always waits to get back to his yard. Good dog, except if he ever has to be boarded or live spend the night somewhere else. Then he'll be in trouble.

Is there no dog park nearby? Buying one of the retractable leashes which allows her to run up to 30 ft or more ahead of you may help since it allows dogs to feel free of a leash.
Since she usually has free run, her holding her urine for long periods is not a good thing........as you know.

Thanks to all who posted. Just reporting back that she is finally doing her thing!

Sometimes our new dog is holding her pee for up to 18 or 19 hours. We let her out ample times and she refuses to go. I have even tried taking her for long walks trying to get her to do her business. When she does I always praise her by rubbing her head and saying "good Potty!!" She is in good health and is drinking plenty of water. We've had her 6 weeks and she came from the shelter. She seems very happy. She came obedient trained, house broken and crate trained. So far this is our only problem and it has me worried.