That's pretty compact as is. Here's one possibility, though (untested):

while ($line1 = <FILE1> && $line2 = <FILE2>) {
    print RESULT $line1, $line2;
}
[download]

The while loop does the equivalent of your defined check.

Update: merlyn points out that && is too high on the precedence scale to work. Use and instead. Also, this code is likely to fail if you hit a line of '0', as the loop actually does a truth-test. Thanks!