it's probably the windows newline characters in there.. try s/[\r\n]+$//; instead of chomp (you could probably change the $/ variable instead -- see perldoc perlvar and perldoc -f chomp).
side note: you can do ./test.plx < symbols.txt instead of the useless cat. note also that this can be written as:
perl -e 's/([\r\n]+)$/ is the symbol$1/' symbols.txt