Não. Isso ocorre por design, e a declaração oficial da Oracle é:
Chrome no longer supports NPAPI (technology required for Java applets)
The Java plug-in for web browsers relies on the cross platform plugin architecture NPAPI, which has been supported by all major web browsers for over a decade. Google's Chrome version 45 (scheduled for release in September 2015) drops support for NPAPI, impacting plugins for Silverlight, Java, Facebook Video and other similar NPAPI based plugins.
Java applications are offered through web browsers as either a web start application (which do not interact with the browser once they are launched) or as a Java applet (which might interact with the browser). This change does not affect Web Start applications, it only impacts applets.
If you have problems accessing Java applications using Chrome, Oracle recommends using Internet Explorer (Windows) or Safari (Mac OS X) instead.
Developers and System administrators looking for alternative ways to support users of Chrome should see this blog regarding Launching Web Start applications.
Junto com a declaração oficial sobre Chrome:
Access websites that use NPAPI
NPAPI plugins can't be enabled, so if you want to use a website that uses an NPAPI plugin, you’ll need to use a different web browser.
O desenvolvedor precisará alterar o funcionamento dele ou você precisará usar um navegador diferente ou um navegador mais antigo e menos seguro.