Q:

What request to call a 

What request would a <input type="checkbox" name="chkbx" checked > return?
Normally I would do something like this:
if(Request["chkbx"] == true)
{
}

But that doesn't work with checkboxes.

A:

In direct response to your question, the key returns true,false as a string in that case. So this is what you want:
if ((Request["chkbx"] as string).Contains("true")) {
}

It is just "false" if not checked.
Ideally though, you would create a model.. 
class Model {
    public bool IsChecked { get; set; }
}

..make your view strongly typed:
@model Your.Namespace.Model

Then use the ...For helpers to bind your model:
@using (Html.BeginForm()) {
    @Html.CheckBoxFor(x => x.IsChecked)
    <input type="submit" />
}

Then in your action method.. you do this:
[HttpPost]
public ActionResult YourMethod(Model model) {
    if (model.IsChecked) {
        // your code here
    }
}

