Make a “exclusive” Post using a custom field

I'd like a custom field, that can only be assigned to one post at a time. Ideally directly from the Dashboard.

Let's say I have a custom field featured post on /post-123 with value true.
If I assign featured post: true to post-111, the value of post-123's featured post-custom field needs to get the value false or deleted entirely.

This means that my custom field can only be assigned to one post.
OR
A custom field with a specified value can only exist once.

Is there a plugin that can do it? Or is it possible with the WordPress plugin Types?

The custom field saving/updating/removing is done in the action hook save_post.

Before updating the current post meta data, we query all other posts that may contain the same meta and remove it case positive.

Basically:

if ( isset( $_POST['exclusive_post'] )  )
{
    // CHECK FOR OTHER POSTS THAT HAVE THE META DATA SET 
    $args = array(
        'numberposts'     => -1, 
        'offset'          => 0,
        'meta_key'        => 'exclusive_post', 
        'post_type'       => 'post', 
        'post_status'     => 'publish' 
    );
    $results = get_posts( $args );
    foreach( $results as $other_post)
    {
        // REMOVE THE META DATA FROM OTHER POSTS
        delete_post_meta( $other_post->ID, 'exclusive_post' );
    }

    // UPDATE THE CURRENT POST META DATA
    update_post_meta( $post_id, 'exclusive_post', $_POST['exclusive_post'] );
} 
else 
{
        // NO POST META DATA IN CURRENT POST, REMOVE META
    delete_post_meta( $post_id, 'exclusive_post' );
}

And here, a full working example using a meta box based in Add a checkbox to post screen that adds a class to the title:

<?php
/**
 * Plugin Name: Exclusive Post Meta Box
 * Description: Creates a custom field that can only be assigned to one post.
 * Plugin URI:  http://stackoverflow.com/q/15721612/1287812
 * Author:      brasofilo
 * Author URI:  https://wordpress.stackexchange.com/users/12615/brasofilo
 */


/* Define the custom box */
add_action( 'add_meta_boxes', 'wpse_61041_add_custom_box' );

/* Do something with the data entered */
add_action( 'save_post', 'wpse_61041_save_postdata', 10, 2 );

/* Adds a box to the main column on the Post and Page edit screens */
function wpse_61041_add_custom_box() {
    add_meta_box( 
        'wpse_61041_sectionid',
        'Exclusive Post',
        'wpse_61041_inner_custom_box',
        'post',
        'side',
        'high'
    );
}

/* Prints the box content */
function wpse_61041_inner_custom_box($post)
{
    // Use nonce for verification
    wp_nonce_field( plugin_basename( __FILE__ ), 'wpse_61041_noncename' );

    // Get saved value, if none exists, "default" is selected
    $saved = get_post_meta( $post->ID, 'exclusive_post', true);

    printf(
        '<input type="checkbox" name="exclusive_post" value="exclusive_post" id="exclusive_post" %1$s />'.
        '<label for="exclusive_post"> This is the one.' .
        '</label><br>',
        checked($saved, 'exclusive_post', false)
    );

}

/* When the post is saved, saves our custom data */
function wpse_61041_save_postdata( $post_id, $post_object ) 
{
      // verify if this is an auto save routine. 
      // If it is our form has not been submitted, so we dont want to do anything
      if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) 
          return;

      // verify this came from the our screen and with proper authorization,
      // because save_post can be triggered at other times
      if ( !wp_verify_nonce( $_POST['wpse_61041_noncename'], plugin_basename( __FILE__ ) ) )
          return;

    // don't run if saving revision.
    if ( 'revision' == $post_object->post_type )
        return;

    if ( isset( $_POST['exclusive_post'] )  )
    {
        // CHECK FOR OTHER POSTS THAT HAVE THE META DATA SET 
        $args = array(
            'numberposts'     => -1, 
            'offset'          => 0,
            'meta_key'        => 'exclusive_post', 
            'post_type'       => 'post', 
            'post_status'     => 'publish' 
        );
        $results = get_posts( $args );
        foreach( $results as $other_post)
        {
            // REMOVE THE META DATA FROM OTHER POSTS
            delete_post_meta( $other_post->ID, 'exclusive_post' );
        }

        // UPDATE THE CURRENT POST META DATA
        update_post_meta( $post_id, 'exclusive_post', $_POST['exclusive_post'] );
    } 
    else 
    {
        // NO POST META DATA IN CURRENT POST, REMOVE META
        delete_post_meta( $post_id, 'exclusive_post' );
    }

}