use warnings;
use strict;
use Data::Dumper;

my %hoh;
push @{$hoh{'this'}->{'that'}->{'theOther'} }, ['eggs', 'bacon', 'cheese'];

print Dumper (\%hoh);

##</code><code>##

$VAR1 = {
          'this' => {
                      'that' => {
                                  'theOther' => [
                                                  [
                                                    'eggs',
                                                    'bacon',
                                                    'cheese'
                                                  ]
                                                ]
                                }
                    }
        };