When I use Chrome to visit a web site that requires Java Plugin, I got a big gray box with a message saying "This plugin is not supported".

Why Java Plugin in not supported in Chrome?

Most likely your Chrome version is 42 or higher and the NPAPI is disabled by the browser. That impacts all plugins (including Java Plugin) who uses NPAPI.

Here is the detailed explanation of what happened to the NPAPI support by Chrome from Oracle Java web site:

The Java plug-in for web browsers relies on the cross platform plugin architecture NPAPI, which has long been, and currently is, supported by all major web browsers. Google announced in September 2013 plans to remove NPAPI support from Chrome by "the end of 2014", thus effectively dropping support for Silverlight, Java, Facebook Video and other similar NPAPI based plugins. Recently, Google has revised their plans and now state that they plan to completely remove NPAPI by late 2015. As it is unclear if these dates will be further extended or not, we strongly recommend Java users consider alternatives to Chrome as soon as possible. Instead, we recommend Firefox, Internet Explorer and Safari as longer-term options. As of April 2015, starting with Chrome Version 42, Google has added an additional step to configuring NPAPI based plugins like Java to run by using chrome://flags/#enable-npapi.