Okay, so I finally got it to work in Chrome. I followed the settings from this web page: https://support.google.com/chrome/answer/142064?hl=en
Specifically, I followed these steps from the above link:
Chrome uses plugins by default on a webpage unless they present a security risk.
Chrome automatically blocks plugins that are out of date or not used by a lot of programs. You can also block plugins yourself any time:
To allow plugins for specific websites only, click Manage exceptions.
Note: You can also reach the plugins page by clicking Manage individual plugins in the "Plugins" section of the Content settings dialog.
I think what finally did it for me was to Manage exceptions. I had already gone into the list and choose to always allow the VMware plugins. What I did under Manage exceptions was add the web site for my VMware Web Client. Example IP Address: https://10.10.10.10:9443. I changed the IP here for security reasons but after typing that in to the box and pressing enter/return, then clicking done, then reloading my VMware Web Client page, I right clicked on my datacenter, deploy OVF, and I wasn't prompted to install the plugin! Success!
I hope this helps someone.