$line =~ tr/\r\n//d; should do what BrowserUK suggested..IIRC, the /d is required to delete characters. Checking the value of $/ would help ascertain why chomp() isn't working the way you expected.
Also, $line =~ s/\r\n$//; would probably more accurately replicate chomp()'s functionality.
Update: Thanks to bart, who reminded me that the $INPUT_RECORD_SEPARATOR is $/, not $\. There still appear to be quite a few incorrect vars floating around this thread.