Number puzzle

Here's a little number puzzle quiz.

Fill in the digits:

   ABC
+DEF
GHI

Where each letter represents a unique digit between 1 and 9, such that all digits are used exactly once.

OR (and this is where it gets interesting...) prove that it's impossible to fill in such digits. (And, "it's too hard" is not a proof that it's impossible)

I came up with this morning while teaching my 2 year old daughter her digits 1 through 9. (No, she didn't solve it). I was writing the digits 1,2,3,4,5,6,7,8,9 in a 3x3 matrix for her and thought it would be cute if the first row plus the second row added to the third row.

I'll leave comments moderated here to prevent folks from giving away the answer. [Update:] I'm getting lots of great responses here and I'm itching to unmoderate the comments. soon...  [Update:] I've published the comments and written a followup post.