Entity reference field with custom class
Inside your tempalate.php file, add the following for that field. This is the standard implementation of theme_field. I added the line if ($delta == 1) $classes .= ' first'; to add the class. 

function yourthemename_field__yourfieldname ($variables) {
  $output = '';

  // Render the label, if it's not hidden.
  if (!$variables ['label_hidden']) {
    $output .= '&lt;div class="field-label"' . $variables ['title_attributes'] . '&gt;' . $variables ['label'] . ':&amp;nbsp;&lt;/div&gt;';
  }

  // Render the items.
  $output .= '&lt;div class="field-items"' . $variables ['content_attributes'] . '&gt;';
  foreach ($variables ['items'] as $delta =&gt; $item) {
    $classes = 'field-item ' . ($delta % 2 ? 'odd' : 'even');
    //add your class here
    if ($delta == 1) $classes .= ' first';
    $output .= '&lt;div class="' . $classes . '"' . $variables ['item_attributes'][$delta] . '&gt;' . drupal_render($item) . '&lt;/div&gt;';
  }
  $output .= '&lt;/div&gt;';

  // Render the top-level DIV.
  $output = '&lt;div class="' . $variables ['classes'] . '"' . $variables ['attributes'] . '&gt;' . $output . '&lt;/div&gt;';


  return $output;
}


Furthermore, you can change this for different view modes and different bundles. The rest is in documentation.