diff --git a/core/includes/form.inc b/core/includes/form.inc
index 6a747b6..9c035b2 100644
--- a/core/includes/form.inc
+++ b/core/includes/form.inc
@@ -1343,7 +1343,11 @@ function _form_validate(&$elements, &$form_state, $form_id = NULL) {
           $elements['#value'] = NULL;
           form_set_value($elements, NULL, $form_state);
         }
-        elseif (!isset($options[$elements['#value']])) {
+        // Throw an error if the submitted #value is not contained in #options,
+        // but only if there actually is a value. A #type 'radios' may not have
+        // a value if it has no #default_value and when it is optional (or only
+        // conditionally required via #limit_validation_errors).
+        elseif (!isset($options[$elements['#value']]) && $elements['#value'] !== '') {
           form_error($elements, $t('An illegal choice has been detected. Please contact the site administrator.'));
           watchdog('form', 'Illegal choice %choice in %name element.', array('%choice' => $elements['#value'], '%name' => empty($elements['#title']) ? $elements['#parents'][0] : $elements['#title']), WATCHDOG_ERROR);
         }
@@ -2809,7 +2813,7 @@ function theme_radio($variables) {
   $element['#attributes']['type'] = 'radio';
   element_set_attributes($element, array('id', 'name', '#return_value' => 'value'));
 
-  if (isset($element['#return_value']) && $element['#value'] !== FALSE && $element['#value'] == $element['#return_value']) {
+  if (isset($element['#return_value']) && $element['#value'] !== FALSE && $element['#value'] === $element['#return_value']) {
     $element['#attributes']['checked'] = 'checked';
   }
   _form_set_class($element, array('form-radio'));
diff --git a/core/modules/system/lib/Drupal/system/Tests/Form/ElementTest.php b/core/modules/system/lib/Drupal/system/Tests/Form/ElementTest.php
index cac8d2c..5bae111 100644
--- a/core/modules/system/lib/Drupal/system/Tests/Form/ElementTest.php
+++ b/core/modules/system/lib/Drupal/system/Tests/Form/ElementTest.php
@@ -62,6 +62,10 @@ class ElementTest extends WebTestBase {
         $expected = array_shift($expected_values);
         $this->assertIdentical((string) $element['value'], $expected);
       }
+      // Additionally verify that there is only one option checked.
+      $elements = $this->xpath('//input[@type=:type and @checked="checked"]', array(':type' => $type));
+      $this->assertEqual(count($elements), 1);
+      $this->assertIdentical((string) $elements[0]['value'], '0');
     }
 
     // Enable customized option sub-elements.
diff --git a/core/modules/system/tests/modules/form_test/form_test.module b/core/modules/system/tests/modules/form_test/form_test.module
index b89426c..67f1d5d 100644
--- a/core/modules/system/tests/modules/form_test/form_test.module
+++ b/core/modules/system/tests/modules/form_test/form_test.module
@@ -1455,6 +1455,7 @@ function form_test_checkboxes_radios($form, &$form_state, $customize = FALSE) {
   $form['checkboxes'] = array(
     '#type' => 'checkboxes',
     '#title' => 'Checkboxes',
+    '#default_value' => array(0),
     '#options' => array(
       0 => 'Zero',
       'foo' => 'Foo',
@@ -1479,6 +1480,7 @@ function form_test_checkboxes_radios($form, &$form_state, $customize = FALSE) {
   $form['radios'] = array(
     '#type' => 'radios',
     '#title' => 'Radios',
+    '#default_value' => 0,
     '#options' => array(
       0 => 'Zero',
       'foo' => 'Foo',