For the fun of it ( and also to show you can seek on DATA )

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1215128

use strict;
use warnings;

my %chapters;
my $previous = undef;
my $buffer;
my $max = 4096;

while(<DATA>)
  {
  if( /^Chapter/ )
    {
    $chapters{$_} = $previous = [ tell(DATA) - length, length ];
    }
  elsif( defined $previous )
    {
    $previous->[1] += length;
    }
  }

use Data::Dump 'pp'; print pp \%chapters; print "\n\n";

for ( sort keys %chapters )
  {
  my ($start, $length) = $chapters{$_}->@*;
  seek DATA, $start, 0;
  while( $length > $max )
    {
    read DATA, $buffer, $max;
    print $buffer;
    $length -= $max;
    }
  read DATA, $buffer, $length;
  print $buffer;
  }

__DATA__
Chapter One
There were lots of monkeys here and they ate all the bananas...
lots more text up to hundreds of words.
Chapter Nine
This chapter has probably 1000 words.
Chapter Two
Here is the text in the second chapter...
Chapter Five
Here is the text in the fifth chapter...
every chapter is of differing length, some long some short.
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