Cathy your so right it is the 'A' chord.

Pressing down the 2nd, 3rd and 4th string on the 2nd fret. It is taught, to use fingers 1,2,and 3.
But of course the mini barre, makes it easier..
Joni Mitchell plays a lot that way, going up and down the fingerboard, also using her thumb.
That would explain how she's able to play with those long finger nails... :D
I hear she does a special tuning, for it to work. And she's been quoted as saying, "it's very tuff on the guitar neck"...