There are numerous chicken stock based soups that also have milk as an ingredient and the milk always seems to curdle - how can I prevent this?
For protection against heat, you can stabalize the milk with starches. (eg, a white sauce made with milk won't curdle, even if you boil it). I unfortunately don't know how much you'd have to add, and of course, it'll end up affecting the texture of your soup).
For soups, you're likely better off making a corn starch/milk slurry before adding the milk, so you don't have to cook it like you would flour to get rid of the raw flour taste.
You may also want to consider the heat that you're cooking the soup at -- you likely want a low simmer, not a full boil.
Milk curdles due to acidity, so if you can raise the pH of the soup by adding something basic, it would help, although it could affect flavor.
The other thing to try is heating the milk to ~90 degrees C before adding it to the soup. This will cause the protein in the milk to change in a way that curdling won't result in as bad a final result--it may in fact appear that the milk hasn't curdled at all.
You can also "temper" the milk (as mentioned by Ocaasi): add a bit of the soup to the milk first; then add the milk-soup mixture to the soup at large. And yes, higher fat milks will tend to work better.
Try adding the milk separately to only a single cup of broth. Stir thoroughly. Then slowly add this to the pot. It will allow the milk to come up to temperature gradually in a less acidic environment. Also, higher fat milk will be less likely to curdle, in case when you said milk you meant something other than milk.