Can you implement WLAN on a ZigBee chip?
No, you can't use a Zigbee specific processor in a 802.11 WLAN. They're not reprogrammable. 

You might want to take a look at the ESP8266, which is a (slow) Wifi module that seems to be reprogrammable. 

Adafruit Link to a Module https://www.adafruit.com/products/2282
Instructables Link to a How-To http://www.instructables.com/id/Getting-Started-with-the-ESP8266-ESP-12/