Create implementation of the side panel using a dialog.

chrome/browser/resources/settings/settings_ui/settings_ui.html

 <link rel="import" href="chrome://resources/cr_elements/cr_toolbar/cr_toolbar.html">
 <link rel="import" href="chrome://resources/cr_elements/icons.html">
 <link rel="import" href="chrome://resources/html/polymer.html">
-<link rel="import" href="chrome://resources/polymer/v1_0/app-layout/app-drawer/app-drawer.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/iron-flex-layout/iron-flex-layout.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/paper-header-panel/paper-header-panel.html">
+<link rel="import" href="/controls/dialog_drawer.html">
 <link rel="import" href="/direction_delegate.html">
 <link rel="import" href="/global_scroll_target_behavior.html">
 <link rel="import" href="/i18n_setup.html">
 <link rel="import" href="/icons.html">
 <link rel="import" href="/settings_main/settings_main.html">
 <link rel="import" href="/settings_menu/settings_menu.html">
 <link rel="import" href="/settings_shared_css.html">
 <link rel="import" href="/prefs/prefs.html">
 <link rel="import" href="/route.html">
 <link rel="import" href="/settings_vars_css.html">
@@ skipping 27 matching lines @@
         font-size: 123.08%; /* go to 16px from 13px */
         min-height: 56px;
       }
 
       .last {
         display: flex;
         justify-content: flex-end;
         width: 100%;
       }
 
-      app-drawer {
+      dialog[is='dialog-drawer'] {
         z-index: 2;
       }
 
-      app-drawer .drawer-header {
+      dialog[is='dialog-drawer'] .drawer-header {
         align-items: center;
         display: flex;
         font-size: 123.08%; /* go to 16px from 13px */
         min-height: 56px;
       }
 
       cr-toolbar {
         @apply(--layout-center);
         --cr-toolbar-field-width: var(--settings-card-max-width);
         background-color: var(--settings-title-bar-background-color);
         color: white;
         min-height: 56px;
         z-index: 2;
       }
 
       cr-toolbar {
         --iron-icon-fill-color: white;
       }
 
-      app-drawer .drawer-header {
+      dialog[is='dialog-drawer'] .drawer-header {
         -webkit-padding-start: 24px;
         border-bottom: var(--settings-separator-line);
       }
 
-      app-drawer .drawer-content {
+      dialog[is='dialog-drawer'] .drawer-content {
         height: calc(100% - 56px);
         overflow: auto;
       }
     </style>
     <settings-prefs id="prefs" prefs="{{prefs}}"></settings-prefs>
     <cr-toolbar page-name="$i18n{settings}"
         clear-label="$i18n{clearSearch}"
         search-prompt="$i18n{searchPrompt}"
         on-cr-toolbar-menu-tap="onMenuButtonTap_"
         spinner-active="[[toolbarSpinnerActive_]]"
         menu-label="$i18n{menuButtonLabel}"
         on-search-changed="onSearchChanged_"
         show-menu>
     </cr-toolbar>
-    <app-drawer swipe-open>
+    <dialog id="drawer" is="dialog-drawer">
       <div class="drawer-header">$i18n{settings}</div>
       <div class="drawer-content">
         <template is="dom-if" id="drawerTemplate">
           <settings-menu page-visibility="[[pageVisibility_]]"
               show-android-apps="[[showAndroidApps_]]"
               on-iron-activate="onIronActivate_"
               advanced-opened="{{advancedOpened_}}">
           </settings-menu>
         </template>
       </div>
-    </app-drawer>
+    </dialog>
     <paper-header-panel id="headerPanel" mode="waterfall">
       <settings-main id="main" prefs="{{prefs}}"
           toolbar-spinner-active="{{toolbarSpinnerActive_}}"
           page-visibility="[[pageVisibility_]]"
           show-android-apps="[[showAndroidApps_]]"
           advanced-toggle-expanded="{{advancedOpened_}}">
       </settings-main>
     </paper-header-panel>
   </template>
   <script src="settings_ui.js"></script>
 </dom-module>