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/**
 * Add the field to the checkout
 */
add_action( 'woocommerce_after_order_notes', 'my_custom_checkout_field' );

function my_custom_checkout_field( $checkout ) {

    echo '<div id="my_custom_checkout_field"><h2>' . __('My Field') . '</h2>';

    woocommerce_form_field( 'my_field_name', array(
        'type'          => 'text',
        'class'         => array('my-field-class form-row-wide'),
        'label'         => __('Fill in this field'),
        'placeholder'   => __('Enter something'),
        ), $checkout->get_value( 'my_field_name' ));

    echo '</div>';

}