Sprinkle chicken with salt, nutmeg, and pepper.
In large nonstick skillet, heat oil.
Brown chicken breasts on each side.
Add jam, tarragon, green onions, and wine.
Cover, reduce heat to simmer, and cook 15 minutes.
Add grapes and cook 5 minutes.
Remove chicken and grapes with slotted spoon and keep warm.
Add milk to the pan.
Turn heat up and reduce, uncovered, until liquids thicken.
Spoon over chicken and grapes and serve.