Then pass in a function reference -- something like this:

sub chunk_at_a_time
{
  my $FH = IO::File->new ...

  my $func_ref = shift;
  my @func_args = @_;
  until ( $FH->eof ) 
  {
    &{$func_ref}(@func_args);
  }
}
...

My_Module::chunk_at_a_time( @file_args, \&some_sub_name, @sub_args);
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(I dashed this off quick -- the syntax may be wrong, but you get the idea.)