Go to Settings (type "chrome://settings" in the address bar or use the menu), click "Advanced Settings," scroll down to "Privacy," and click "Content Settings..." and make sure that either "Run automatically" or "Click to play" is selected. You may need to click "Manage exceptions..." and make sure that minecraft.net isn't on the list, or if it is, that it's marked "Allowed."
Then click on "Disable individual plug-ins..." (I know, it's badly named.) and make sure Java is in the list and is enabled.
But do not check the "Always allowed" box. Java has some long-standing security problems, and attackers can potentially take over your computer with it, even with the added safeguards the Chrome puts in place.
If everything looks good, then something went wrong with the plugin installation. Uninstall Java any any other tripe it came with, reboot if necessary,
and try again.