In a pinch, a good trick can be to use cat largefile.txt |perl yourscript.pl. That's what I used to do on Solaris with an old Perl. A version of Perl without >2GB file support can read from a pipe just fine, even if that pipe happens to contain a file larger than 2GB.

The real solution, as everybody else has said, is get a copy of Perl with large files support, either by getting it in a package or by recompiling it.