Add a custom select field to the WooCommerce checkout page

functions.php

<?php
//* Do NOT include the opening php tag shown above. Copy the code shown below.

//* Add select field to the checkout page
add_action('woocommerce_before_order_notes', 'wps_add_select_checkout_field');
function wps_add_select_checkout_field( $checkout ) {

	echo '<h2>'.__('Next Day Delivery').'</h2>';

	woocommerce_form_field( 'daypart', array(
	    'type'          => 'select',
	    'class'         => array( 'wps-drop' ),
	    'label'         => __( 'Delivery options' ),
	    'options'       => array(
	    	'blank'		=> __( 'Select a day part', 'wps' ),
	        'morning'	=> __( 'In the morning', 'wps' ),
	        'afternoon'	=> __( 'In the afternoon', 'wps' ),
	        'evening' 	=> __( 'In the evening', 'wps' )
	    )
 ),

	$checkout->get_value( 'daypart' ));

}