Chrome no longer supports Silverlight. Rather, Chrome no longer supports the underlying protocol that Silverlight relies on, NPAPI. At the moment they have just disabled NPAPI, You can reenable it by:
Entering chrome://flags/#enable-npapi
in Chrome's address bar
Clicking 'enable' under 'Enable NPAPI'
Clicking the 'relaunch now' button.
Once you do that, the Silverlight plugin will be available again in the plugins section (along with many other plugins). This is only a temporary solution, however, as they plan on removing that option entirely by, I believe, September.
I have read elsewhere (see this article by Chris Merriman) that Microsoft's response was that there are other Silverlight capable browser alternatives to Chrome. I think you can take that to mean that Microsoft has no intention of creating a new Silverlight plugin for Chrome that does not rely on NPAPI. In other words, Chrome will likely never support Silverlight again.
NPAPI was completely removed from Chrome in version 45 released on Sept. 1st 2015. It is no longer possible to run Silverlight (or any other plug-ins that rely on NPAPI) in Chrome.