You'll need to find a treeview jquery plugin that will work for you, then bind that to a controller in MVC that can behave the way you're looking for.
Make sure your html is rendering out the placeholder for the children (or that the jQuery plugin knows how to add the children on its own).
You'll have to either provide the treeview an url with a specific set of parameters, or respond to event handlers and make calls to get children.
When looking for a treeview plugin, your life will be easier if you find one that supports the async loading of child nodes.
If you had to roll your own, you might have a div with an ID of ChildNode-1 and the call might look something like the following in MVC:
$("#ChildNode-1").load("/[your_controller]/GetNode", {nodeId:1});
On your controller you would have a method called GetNode that returns a PartialViewResult. It would accept a parameter of type int called nodeId. Mark it with the attribute [HttpPost]. jQuery wizardry handles the post action and MVC magic and reflection take care of the rest. Your PartialViewResult would also have to return more nodes formatted to make more submissions per the above.
Cheers,
-jc