Here is a solution ...

// First create your array of terms
$terms = array(
  'level1-1' => array(
    'level2-1' => array(
      'level3' => array(),
    ),
    'level2-2' => array(
      'level3' => array(
        'level4' => array(),
      ),
    ),
  ),
);

// Create your vocabulary.
// First check if the vocabulary exists otherwise an error will be thrown when trying to create it.
$vocabs = taxonomy_get_vocabularies(NULL);
$vocab = new stdClass();
foreach ($vocabs as $vocab_object) {
    if ($vocab_object->machine_name == 'vocab_short_name') {
        // Vocab found.  Grab the object.
        $vocab = $vocab_object;
        break;
    }
}
// If the vid is not set then create the vocab.
if(!isset($vocab->vid)) {
    $vocab = new stdClass();
    $vocab->name = 'Vocabulary Name';
    $vocab->machine_name = 'vocab_short_name';
    taxonomy_vocabulary_save($vocab);
}
// Recursive function that will create the hierarchical terms.
mymodule_add_hierarchical_terms($terms, $vocab->vid);


function mymodule_add_hierarchical_terms($vocab, $vid, $parent = null) {

  foreach($vocab as $term_name => $term) {
    // Create the term
    $term_object = new stdClass();
    $term_object->vid = $vid;
    $term_object->name = $term_name;
    if(isset($parent)) {
        $term_object->parent = $parent;
    }
    taxonomy_term_save($term_object);
    
    if(is_array($term)) {
      // Recursively call the function.
      mymodule_add_hierarchical_terms($term, $vid, $term_object->tid);
    }
}
}

Here is a solution ...

// First create your array of terms
$terms = array(
  'level1-1' => array(
    'level2-1' => array(
      'level3' => array(),
    ),
    'level2-2' => array(
      'level3' => array(
        'level4' => array(),
      ),
    ),
  ),
);

// Create your vocabulary.
// First check if the vocabulary exists otherwise an error will be thrown when trying to create it.
$vocabs = taxonomy_get_vocabularies(NULL);
$vocab = new stdClass();
foreach ($vocabs as $vocab_object) {
    if ($vocab_object->machine_name == 'vocab_short_name') {
        // Vocab found.  Grab the object.
        $vocab = $vocab_object;
        break;
    }
}
// If the vid is not set then create the vocab.
if(!isset($vocab->vid)) {
    $vocab = new stdClass();
    $vocab->name = 'Vocabulary Name';
    $vocab->machine_name = 'vocab_short_name';
    taxonomy_vocabulary_save($vocab);
}
// Recursive function that will create the hierarchical terms.
mymodule_add_hierarchical_terms($terms, $vocab->vid);


function mymodule_add_hierarchical_terms($vocab, $vid, $parent = null) {

  foreach($vocab as $term_name => $term) {
    // Create the term
    $term_object = new stdClass();
    $term_object->vid = $vid;
    $term_object->name = $term_name;
    if(isset($parent)) {
        $term_object->parent = $parent;
    }
    taxonomy_term_save($term_object);
    
    if(is_array($term)) {
      // Recursively call the function, passing the term id of the parent.
      mymodule_add_hierarchical_terms($term, $vid, $term_object->tid);
    }
  }
}