Troubleshooting:
I have since unchecked the option Enable Java content on the browser in System Preferences > Java > Security - I will report back if the prompt still reappears, but I think it should be gone now.
Follow up:
I have since sent a feedback to Apple and I recommend you guys send it too, more people reporting will get Apple's attention on the issue.
Issue:
For me, this issue started after updating to Yosemite, I keep getting a prompt window on Chrome 38.0.2125.122 with a message "To view this web content you need to install the Java Runtime Environment, but I do have Java installed."
Hardware/Software:
Macbook Air Mid 2013 1.3Ghz 8GB RAM 120GB SSD / Mac OS X Yosemite 10.10