A little recursive sub to compile this into the right format:

use strict;
use warnings;

use Data::Dumper qw( Dumper );

my %tree;

while (<DATA>) {
   chomp;
   my $p = \%tree;
   foreach (split(qr{\s*/\s*}, $_)) {
      $p = $p->{$_} ||= {};
   }
}

sub re_format {
    my $data = shift;
    my $out = [];
    for my $key (keys %$data) {
        my $temp = { name => $key};
        if (keys %{ $data->{$key} }) {
           $temp->{children} = re_format($data->{$key})
        }
        push @$out, $temp;
    }
    return $out;
}    

print Dumper('First Step' => \%tree, 'Final' => re_format(\%tree));

__DATA__
one
foo / bar
foo / baz
foo / qux / two
foo / qux / three
foo / qux / four
five
[download]

Thank you very much Eric.

No ... I spoke too soon again. The reformatted data is now out of order. The reason I use a List of Hashes is because I have to preserve the same order.

In order words, %tree really needs to be @tree.

Can anybody help me? I have spent far too much time trying to solve this problem. :(

But thanks anyways -- good ideas in there.

Are you suggesting that with a few modifications that I can use your code snippet to achieve my goal? Because I don't see how I can push the children onto their parents using your code (which doesn't produce the output I need).

Yes, this kind of question has been discussed before. You may also be interested in nodes referenced in that thread. Two modules, that were mentioned in the discussion and that could come useful to make "structured text" into a complex data structure are Data::Hierarchy and Data::Diver.