I looked at the FASTA format and it is ASCII, however there could be some other issue here with the program that generated this file. Can you open the original file in the text editor, eg WordPad and see the characters displayed properly? chomp() should not affect this. This "I see bizarre characters in the texteditor" is sounding like a big clue to me that format is wrong and your small example works because it is ASCII?
update: there are a bunch of modules to mess with this BIO FASTA format. Search CPAN for "FASTA". But this sounds easy enough to figure out without a module.