What's the best fat for frying chicken?
Lard? Shortening? Veg oil or a combo or something else entirely?
If you need to deep fry, please pay attention, as monku, has referred to, to the smoking point. What tastes good may be deleterious to your health, long term. Free radicals form for unstable oils, those that don't handle a high heat well.
Due a google search on oils to get more information. Supposedly, refined avocado has one of the highest smoking points for vegetable oils, while some of the other well known veg oils have a slightly lower smoking point ... refined soy, corn, refined high oleic safflower and sunflower ... this is just a sample.
No question about Lard resulting in tasty fried skin ... coconut oil is supposed to be good, too.
The rule of thumb is that for very high heating, refined oils are better suited, for no or low heating, unrefined maintains the nutrients in oil more.
If you want to stay superhealthy, explore various cook's recipes on simulating the "fry" texture and taste through baking the food.
My favorite oil for stir frying is sesame oil (not the toasted sesame version). Oil used for deep frying really does affect the quality of the resulting dish. I shudder to think of restaurants that use cheap commercial oils that have been superheated during their production, resulting in a potentially harmful product.
If health and free radicals are a concern, all liquid oils are a poor choice. Solid saturated fats will always provide more stability than liquid less saturated ones. Artifically saturated trans fats (traditional shortening) are to be avoided, but, other than those, any saturated fat would make a healthy (and delicious) choice:
Lard is an excellent choice, although I would probably seek out an unhydrogenated brand or possibly even render the pork fat myself.
Throwing the diet out the window, mine would be, Lard!
Peanut oil is my second, but that could be subject to an allergy alert concerning other family members. I would then substitute for a pure Canola oil, in that case.
3rd (or 4th) is those better grades of solid vegetable shortenings.
I am going to add a bit about the lard, as to me, it makes the best southern style or milk gravy if pan fried.
Lard, lard, lard, oh Lordy, lard, lard, lard!
Having said that brings into question what you mean by "best"!