Add chrome.windows.update({focused:true});

chrome/common/extensions/api/extension_api.json

 [
   {
     "namespace": "extension",
     "unprivileged": true,
     "types": [
       {
         "id": "MessageSender",
         "type": "object",
         "description": "An object containing information about the script context that sent a message or request.",
         "properties": {
@@ skipping 710 matching lines @@
         "description": "Updates the properties of a window. Specify only the properties that you want to change; unspecified properties will be left unchanged.",
         "parameters": [
           {"type": "integer", "name": "windowId", "minimum": 0},
           {
             "type": "object",
             "name": "updateInfo",
             "properties": {
               "left": {"type": "integer", "optional": true, "description": "The offset from the left edge of the screen to move the window to in pixels."},
               "top": {"type": "integer", "optional": true, "description": "The offset from the top edge of the screen to move the window to in pixels."},
               "width": {"type": "integer", "minimum": 0, "optional": true, "description": "The width to resize the window to in pixels."},
-              "height": {"type": "integer", "minimum": 0, "optional": true, "description": "The height to resize the window to in pixels."}
+              "height": {"type": "integer", "minimum": 0, "optional": true, "description": "The height to resize the window to in pixels."},
+              "focused": {"type": "boolean", "optional": true, "description": "It true, brings the window to the front. If false, brings the next window in the z-order to the front."}
             }
           },
           {
             "type": "function",
             "name": "callback",
             "optional": true,
             "parameters": [
               {
                 "name": "window", "$ref": "Window"
               }
@@ skipping 3399 matching lines @@
         "name": "setStoreLogin",
         "description": "Set a preference value with the store login.",
         "parameters": [
           { "name": "login", "type": "string" },
           { "name": "callback", "type": "function", "optional": "true" }
         ]
       }
     ]
   }
 ]