Jobim? What does he know?

I'd call it either G#dim7, or E7b9/G#. (There's no D in that shape, but there is in the melody.)
That's because I see it in the context of A minor, as a vii or V chord (from the A harmonic minor scale). Dim7 chords can often have extensions a half-step below a chord tone, which aren't necessarily mentioned in the symbol - and in this case the E is of course a melody note, the chord could be played without it.
I'm sure there was a lengthy discussion on this chord (not just what it should be called, but what its function is) a while back over on AllAboutJazz, but damned if I can find the thread now.
Here's one of Jobim's own arrangements of the tune (maybe the one Gerard45 saw), where he calls the first chord D9, and the second one Abdim(6):
Jobim's manuscripts - Jazz Bulletin Board
(I tried accessing the site linked to there, but have had problems - not all scores are viewable even after registering)
Here's an arrangement by Paulo Jobim, calling chord 2 (more or less) the way I would:
http://www.jobim.org/xmlui/bitstream...jpg?sequence=1
Lastly, although I couldn't find the Corcovado thread, here's a great one on How Insensitive, which has the same opening sequence:
How Insensitive - Jazz Bulletin Board