Check whether user has a Chrome extension installed

Chrome now has the ability to send messages from the website to the extension.

So in the extension background.js (content.js will not work) add something like:

chrome.runtime.onMessageExternal.addListener(
    function(request, sender, sendResponse) {
        if (request) {
            if (request.message) {
                if (request.message == "version") {
                    sendResponse({version: 1.0});
                }
            }
        }
        return true;
    });

This will then let you make a call from the website:

var hasExtension = false;

chrome.runtime.sendMessage(extensionId, { message: "version" },
    function (reply) {
        if (reply) {
            if (reply.version) {
                if (reply.version >= requiredVersion) {
                    hasExtension = true;
                }
            }
        }
        else {
          hasExtension = false;
        }
    });

You can then check the hasExtension variable. The only drawback is the call is asynchronous, so you have to work around that somehow.

Edit:
As mentioned below, you’ll need to add an entry to the manifest.json listing the domains that can message your addon. Eg:

"externally_connectable": {
    "matches": ["*://localhost/*", "*://your.domain.com/*"]
},

2021 Update:
chrome.runtime.sendMessage will throw the following exception in console if the extension isn’t installed or it’s disabled.

Unchecked runtime.lastError: Could not establish connection. Receiving end does not exist

To fix this, add this validation inside the sendMessage callback

if (chrome.runtime.lastError) {
    // handle error 
}