wordpress widget textbox in the sidebar

I have a normal textbox widget that I am using in certain sidebars. The text widget generates a div within a ul. Is there anyway to make the widget generate another ul li instead?

<ul><h3>Heading</h3>            <div class="textwidget">

check your sidebar.php and functions.php of the theme, the sidebar define the markup outside the widget; the function register_sidebar() defines the markup before content of the widgets; this markup you must change.
See the codex for this function: codex register_sidebar()

Edit

Specifically, you need to look at the before_widget and after_widget parameters of the register_sidebar() arguments array.

If the register_sidebar() call looks like this:

register_sidebar(array( // Right Column widget area
    'name'=>'Sidebar Right',
    'id'=>'sidebar-right',
    'description' => 'Right-column, half-width sidebar in three-column layout',
    'before_widget' => '<div id="%1$s" class="widget %2$s">',
    'after_widget' => '</div>',
    'before_title' => '<div class="title">',
    'after_title' => '</div>',
));

Then change it to this:

register_sidebar(array( // Right Column widget area
    'name'=>'Sidebar Right',
    'id'=>'sidebar-right',
    'description' => 'Right-column, half-width sidebar in three-column layout',
    'before_widget' => '<li id="%1$s" class="widget %2$s">',
    'after_widget' => '</li>',
    'before_title' => '<div class="title">',
    'after_title' => '</div>',
));

Specifically, you’re changing this:

    'before_widget' => '<div id="%1$s" class="widget %2$s">',
    'after_widget' => '</div>',

To this:

    'before_widget' => '<li id="%1$s" class="widget %2$s">',
    'after_widget' => '</li>',