I'm really craving risotto but I don't have any wine in the house at the moment. I do have white balsamic vinegar, however.
Risotto generally refers to cooking short (or sometimes medium) grain rice, such as Arborio, in some kind of broth/stock until the base becomes creamy. Anything after that is strictly whatever flavors you prefer. There are classic additions past that - such as white wine, hard cheeses, mushrooms, etc - but the sky is the limit.
If it sounds good to you, take a small bit of the risotto base, mix a little of your desired ingredient in and the sample it. If it tastes good, expand on it! At worst you've messed up a small portion of the dish, at best you look like a culinary genius!
Would white balsamic vinegar taste good? Sound good to me!
Really, the wine step is just for the purpose of deglazing the pan after you sautee the rice in the butter, so the specific liquid doesn't matter very much. I use whiskey sometimes, depending on what kind of risotto I'm making (whiskey and scotch are both amazing for mushroom risotto).
One thing to consider: balsamic is quite high in sugar, so don't wait too long before you start adding broth, or it will stick to the pan.
It should work fine, and be quite good. I'd go easy on it, though, as it has more flavor and acid than white wine. Try cutting it 50/50 with water or some of your stock.
I have tried using dark balsamic and red wine vinegar at the deglazing stage and have gotten totally acceptable results. I'd agree with @adam to use half the amount called for of wine and stir continuously until the vinegar dissolves. White wine is always better though, in my opinion.