Not now may be from October onwards once Google launches their Chrome Web Store which contains free and paid games which you can install and play in your Google Chrome browser.You can able to purchase paid games from Chrome Web store you can pay them through Google Checkout.

Chrome Web Store allows to  install and play games  in Chrome

Number one search engine giant, Google now got its eye on browser games market, according to 1up gaming website Google to launch web app store this October.Google emphasizes why developers should create games for app store because of Google Chrome’s speed and its benefits for browser gaming.

Google Chrome new tab page with Google web apps and link to Google Chrome app store

We already covered how to install Google Web apps in Google Chrome, these web apps can be installed from new tab page .The shortcut icons for apps installed from Web store will appear on new tab page.At present in developer channel after installing Google web apps  Chrome Web Store icon  as shown above opens Chrome extensions page.

Once Chrome Web Store launched Chrome Web Store will be directly accessed from Chrome Web Store icon in the new tab page.

You can read more about Chrome Web store here.