open admin/links.contact.php

find the following line of code:

Code:
$message = zen_db_prepare_input($HTTP_POST_VARS['message']);
below this line add the following

Code:
$html_msg['EMAIL_MESSAGE_HTML'] = $message;

Find the following code:

Code:
zen_mail($mail_query->fields['links_contact_name'], $mail_query->fields['links_contact_email'], $subject, $message, STORE_OWNER, STORE_OWNER_EMAIL_ADDRESS);
Change it to read as follows:
Code:
zen_mail($mail_query->fields['links_contact_name'], $mail_query->fields['links_contact_email'], $subject, $message, STORE_OWNER, STORE_OWNER_EMAIL_ADDRESS, $html_msg);
Save the file and upload to your server