For those who are having trouble with fatal error: ESP8266WiFi.h: No such file or directory
, you can install the package manually.
You may still need to have the http://arduino.esp8266.com/stable/package_esp8266com_index.json package installed beforehand, however.
Edit: That wasn't the full issue, you need to make sure you have the correct ESP8266 Board selected before compiling.
Hope this helps others.