There are a number of free chat services designed specifically for Tumblr. You can add a chat feature to your blog by copying some HTML code and pasting it into your Custom HTML editor on Tumblr. This gives visitors the ability to chat via text in real-time on your Tumblr page.
Visit the Babblr webpage (link in Resources) and copy the chat button HTML from Option 2, so that it is visible on your public Tumblr page. Go to your Tumblr dashboard and click "Customize." Select "Custom HTML" and paste the code into the text editor, right before the "