Urine on Leather Chair- Help!

STOP! DO NOT PUT VINEGAR ON YOUR LEATHER!!!!!!!!!!!!!!!!
It sounds like you have a full grain leather which is a natural leather without plastic chemicals coated on the surface.
This type of leather will darken if it gets wet and also gradually get darker where your body oils touch it regularly.
This is not a defect - it is called patina and will eventually weather into an antique looking finish. If you never want your leather to change color - then next time buy the less expensive, more processed type.
Meanwhile - you can wipe down the entire area with water so that it doesn't look like an obvious " OOopsie!"
You should purchase a good leather conditioner for general maintenance every 6 months. I think Restoration Hardware sells leather conditioner - also Maguire's is a good brand - you should be able to find it at a good hardware store or upholstery shop.
Also, keep your leather out of direct sunlight and dust regularly to prevent scratches and drying/cracking on the surface.
P.S. if the leather really got soaked - the dark spot will lighten a little as the water evaporates out - but it will take a few weeks. You may see a white chalky film develop - that's from the salts in the pee as well as the salts used to tan the leather - wipe it off with a wet cloth and let it dry in a well-ventilated area.

I would call a professional upholsterer or shoe repairer for advice--and the sooner the better! I would be concerned about a smell and deterioration of the leather, as well as the appearance. If you can't remove the stain, maybe there is a way to darken the entire chair so that it doesn't show so much.
Good Luck!

Just wipe it down with white vinegar and water. And unless you're one of those parents who covers everything with plastic and won't let the kids go into the living room, you'd better get used to stuff looking "awful!"

The advise on the shoe repair person is good. I was going to add a leather conditioner that has mink oil in it. I've used that on leather; it does darken the leather but in your case that might be good as it may help with the blending in of the color. Double check with a professional leather person. Good luck.