I'm all out of white wine, what would be a good substitute? I have both red wine and white wine vinegar. Thanks!

I would opt for vegetable or mushroom stock/broth.

White (dry) vermouth is a cooks best friend.
If using a vinegar, add in a bit at a time (eg, 1 tablespoon at a time), taste, to make sure you do end up with too much acid taste.

p.p.s. This is just me speaking, but I always think it's great for people to add their experience in the comments to the poster's recipes. They help other readers a lot - I always spend a lot of time reading comments before I cook - always pays off. Meaning - add a comment to the recipe about how you deal with the wine substitution and if vinegar is OK! Cheers ;-)

p.s. For such a small amount of wine (1/3 cup), you could also substitute vermouth or madeira. Or any kind of broth - chicken, vegetable or beef.

Since the recipe only calls for 1/3 cup wine, I think you're OK with white wine vinegar BUT I would start with less than 1/4 cup white wine vinegar, stir and give it a few minutes to incorporate, taste and decide. If it seems too acidic, add a tiny amount (a teaspoon) of honey. If you don't have honey, a small pinch of sugar will do. (There is sugar in wine.)
http://food52.com/recipes/25556-chestnut-and-chickpea-soup