A tenderloin chain is a piece of the tenderloin that runs along one side. It's much tougher than the loin itself, and most recipes ask you to "remove and save for another use" but don't give much advice on what that other use is. If I'm breaking down a lot of tenderloins and have a lot of chains I will grind them (they make awesome burgers) but since I only had one I decided to braise it with dried mushrooms and red wine.
The chain has a lot of fat and connective tissue, which in my mind makes it perfect for a braise. After removing some of the fat and breaking the chain down into pieces I was left with this.
I prepared this on Monday and we ate it on Thursday, it keeps really well in the fridge. Reheat, and if you want you can thicken the sauce by removing the meat and adding a beurre manié (aka a paste made from equal parts flour and butter) or any other thickening method you prefer. I also added a spoonful of sour cream, just to give it some richness.
I served this dish with egg noodles, but boiled potatoes would also be good.
One of the best parts of butchering larger cuts of meat is you can really use all of the bits and pieces. Grilling a perfect filet can be easily taught to just about anyone, but knowing all of the cuts takes a little more effort. Although that effort is greatly rewarded with meals like this.