Heat oil in large, heavy skillet over moderate heat 2 minutes. Add mushrooms, onion, garlic, marjoram, thyme, and pepper and cook, stirring often, until the juice released from the mushrooms evaporates, about 5 minutes.
Add chicken, alfredo sauce, and wine; adjust heat so mixture bubbles gently, then cook, stirring frequently and breaking up chicken, until steaming, about 3 minutes.
Add asparagus, distributing evenly over surface of mixture, cover and cook just until crisp-tender, 2 to 3 minutes; no longer or asparagus will become mushy.
Make a bed of rice on heated deep platter, spoon chicken mixture on top, and serve.
Al Dente Make-Ahead Rice:
Bring water to rapid boil in large (at least 4 1/2-quart), heavy saucepan over high heat.
Add rice, stir well, and then return to rapid boil. Adjust heat so water stays at gentle but steady ripple and cook uncovered until all water is absorbed, about 20 minutes. Do not stir.
Fluff rice gently with fork and cool 1 hour. Do not cover.
Fluff rice gently again, then spoon lightly, do not pack, into plastic storage containers, snap on lids, label, and date. Set in refrigerator or freezer.
To reheat refrigerated or frozen rice, pile rice in large fine sieve, fork lightly apart and balance sieve in top of large, heavy saucepan over 2-inches boiling water. Cover loosely with lid or foil and steam until just heated through, 3 to 5 minutes, but times will vary according to amount of rice being reheated and whether it's refrigerated or frozen. Fluff with fork and serve.