Step 1Trim the stem ends of the endive. Cut each head lengthwise into quarters, and cut away the solid core. Slice the endive into thin, lengthwise ribbons. Trim any tough stems and faded leaves from the watercress, and tear into bite-sized pieces. (This dish can be prepared to this point a day ahead and refrigerated in a tightly covered container.)
Step 2When almost ready to serve, prepare the vinaigrette by blending the mustard, vinegar, salt, oil and chives. You can do this in a small blender jar or by shaking vigorously in a small, tightly sealed jar.
Step 3Combine the endive and watercress in a large mixing bowl, and dress with about two-thirds of the vinaigrette. Toss to coat lightly, and thoroughly combine the endive and watercress. Arrange in a layer on a large platter.
Step 4Pit and peel the avocados and cut into large dice. Place the avocado in the mixing bowl and dress with half the remaining vinaigrette. Stir gently to coat lightly without breaking up the avocado, and spoon in a single layer over the watercress and endive.
Step 5Place the crab in the mixing bowl, add the remaining vinaigrette and toss gently to coat lightly without breaking up the crab pieces. Arrange the crab in a layer on top of the avocado, sprinkle with the remaining chopped chives and serve immediately.