Apparently they do. A quick search on the Internet and I found this recipe, for Chicken braised in a red wine sauce. I read through the comments and they all seemed to like it, however, it sounded like most reduced the amount of sugar in the sauce.
http://allrecipes.com/Recipe/chicken-and-red-wine-sauce/detail.aspx
Thank you for that link to the red wine chicken recipe. I think that is what I am going to do this evening. I will use the suggestions provided in the second comment. I am signed up on that site and should have checked it out earlier.
Here is another recipe I found on the page you linked to. I will save and try next year when I have fresh figs to use from my tree. Yummm.
Ooops forgot the link.
http://allrecipes.com/recipe/chicken-with-figs-in-a-port-wine-sauce/detail.aspx