My experience with HTML::TreeBuilder showed me that I should use HTML::TreeBuilder::XPath which of course I would recommend you use also.

( HTML::TreeBuilder is nice but HTML::TreeBuilder::XPath is sufficiently abstract in order to be elegant )

Let's see how your code would look if you would use above mentioned module :

  1  #!/usr/local/bin/perl
  2  use strict;
  3  use warnings;
  4  use LWP::Simple;
  5  use HTML::TreeBuilder::XPath;
  6  use Data::Dumper;
  7  use feature 'say';
  8  my $url="http://www.ebi.ac.uk/thornton-srv/databases/cgi-bin/pdbs
+um/GetPage.pl?pdbcode=1r9t&template=main.html";
  9
 10  my $p = HTML::TreeBuilder::XPath->new_from_content(get($url));
 11
 12  my @chain_tags = $p->findnodes("//td//a[contains(\@href,'chain=')
+]");
 13  my @chains = map { $_->attr('href') =~ /chain=(\w)/ } @chain_tags
+;
 14  say " Number of chains : " . scalar @chains;
 15  say @chains;
[download]

EDIT:small adjustments

OUTPUT:

 
Number of chains : 11
AABCEFHIJKL
[download]

First of all we have simplified the code from 33 lines to 15 lines. Second , we maintained the meaning of the code , which was

"Give me the a tags which have attribute href which matches regex "&chain=(\w)" so that the a tags have a parent tag td. Now take those a tags and apply a regex on their href attribute and take the word after the chain= substring".

That is exactly what this XPath query says => //td//a[contains(\@href,'chain=')]

I have also used this Firefox addon to check that my XPath was right.

If you're interested in reading more about XPath read here and here.

You also have a mistake in your code , you delete the HTML::TreeBuilder object after the first iteration of the for loop.

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