Adobe Flash Player no longer usable in Chrome Browser?

I have a white macbook from mid 2009 running on Leopard (OS X. 10.5.8). I am also using the Chrome browser, and got an alert about a month ago saying that my operating system was too old so Chrome will no longer be receiving updates. However, as of today this means that Adobe Flash Player no longer updates itself in the browser so I can no longer use it when I surf the web. I also checked if the Flash player was disabled in the plugin list and it does not even appear there. Do I have to update to Snow Leopard so that Flash can update itself in Chrome? Thank you for your help!