I don't think you need PHP for that. With new WebRTC protocol, you can built it with few lines of javascript. Here is one of the example I found using quick google, https://github.com/keithnorm/simple-webrtc-video-chat
I need something like: http://www.videochatscript.com/videochat-script-overview.html But the proble is this company isn'working anymore since 2010 as I see in their copyrights.
In your case you need quite an investment. I'm unfamiliar with current "popular" scripts in this market, but have developed a fair bit in video streaming lately. You are probably going to need a WowZa or Red5 streaming server.
You can download and try this WP based solution for free: https://wordpress.org/plugins/ppv-live-webcams/
You can also make a test with Bistri SDK: Bistri's SDKs : http://developers.bistri.com/docs-and-examples/
I see a lot of people recommending WebRTC without even knowing the limitations of the protocol... First and foremost while WebRTC works great and on paper seems like the best solutions it's not widely supported so expect a LOT of your visitors to have accessibility issues IF their browser even supports it! Right now we are at an awkward stage. WebRTC will be something that can be used but not yet. Whether you want to believe it or not Flash is your friend when building Video Chat applications. You can take a look at FMS, Wowza, and Red5 but there's not a quick and easy plug n play solution! It also won't be supported on Mobile Platforms so you will need to get super creative and smart or build a separate app. On second thought...between major compatibility and development issues and bandwidth consumption and heavy resource usage you may want to sleep on this idea for a while... The Internet is also not really going the direction of Video Chatting anymore... There's only a small niche community who will be interested. And half of them just want to show their penis to underage boys and girls. Sleep on it please.