[daysinthewake]

Or, without ridiculous enharmonic obsessiveness, and without claiming that it's just a name - there's no such thing as a sharpened third, it's just a perfect fourth.
There is such a thing as quartal harmony, which sounds like it's from Star Trek, where you build chords as fourths rather than thirds, but it's a bit different - and might not technically exist.....

Anyway, augmented chords pretty much come from building chords from the harmonic minor scale, rather than the major scale.

So in A harmonic minor, there are the notes a, b, c, d, e, f, g#, a
(start it on c to get the augmented scale.)

If you build chords from that you get:

A minor
B diminished
C augmented <---here it is!
D minor
E major
F major
G# diminished

or if you wanna delve further into what you can get out of the scale you can even get more than one chord on some degrees of the scale, and some interesting alterations. I love the Fmin -Amin progression. You also get the diminished chord trick, where there are four diminished chords a minor third apart with exactly the same notes, which leads to some fascinating moves.

I put some of the cool ones below.

Amin; A min/maj 7
Bdim7
Caug
Dmin; Ddim7; Dmin7#11
E7; E7b9; Eaug; Eaug+b9; Eaug+dom7b9
Fmaj; Fmin; Fdim7; Fmaj7#9
G#dim7; G#aug;

Most of them are sweeter than they look too. They're not just crazy dissonant jazz chords, they've got a lovely augmented exotic feel to them.

Apart from Fmaj7#9. It is to my ears the most creepy, weird and unnatural chord in the whole of music =)