Can a ESP8266 and a HC-SR04 be friends? I have some existing code that I've been using with an Uno and a HC-SR04. In order to make my project less expensive, I'm trying to port everything over to a ESP8266-01.

The last hang up I've been running into is that it appears that the ESP8266 doesn't support the pulseIn function.

duration = pulseIn(echoPin, HIGH);


Any idea on how I can change the pulseIn function with interrupts or something else?

Lastly I've done a lot of searching for using a HC-SR04 with a ESP8266 and while there are a couple examples out there, I haven't seen anyone do it with Arduino code...
pulseIn() is actually a very simple function.  As long as there is a microseconds counter of some form available you can easily enough roll your own.

Also, I don't know which implementation of the ESP8266 plugin you are using, but the one I use has pulseIn available.