Why do you chomp($line) only to add the linefeed again when printing?

It looks that you could simplify your code to

open (ERRFILE, ">error.log");

open (LOGFILE "/tmp/app.log");
while (<LOGFILE>) {
    print ERRFILE $line if /xception/;
}
[download]

All you have to do then is print some linefeeds when you start a new exception.