In a small bowl, whisk together the vinegar and mustard. Pour in the olive oil in a slow, steady stream, whisking constantly; season with salt and pepper.
Slice off both ends of each tangerine; place cut side down on a cutting board. Cut off the peel and white pith in strips and discard. Hold the tangerine and, working over a serving bowl, make a cut on either side of each segment to free from the membrane and let the segments fall into the bowl.
Add the escarole, endive, radicchio, pecans and cheese to the tangerines. Add the vinaigrette and toss. Top with the chives.