Is it possible to draw a diagonal line using CSS3?

yes it is, there is more then one possibility:

You could use a hr element or a other element and rotate it. Here is a demo:

And yes it works in IE to :)

http://jsfiddle.net/LqFAX/

   -moz-transform: rotate(7.5deg);  
     -o-transform: rotate(7.5deg);  
-webkit-transform: rotate(7.5deg);  
    -ms-transform: rotate(7.5deg);  
        transform: rotate(7.5deg);  
           filter:  progid:DXImageTransform.Microsoft.Matrix(sizingMethod='auto expand',  
                  M11=0.9914448613738104, M12=-0.13052619222005157,M21=0.13052619222005157, M22=0.9914448613738104);
     -ms-filter: "progid:DXImageTransform.Microsoft.Matrix(M11=0.9914448613738104, M12=-0.13052619222005157, M21=0.13052619222005157, M22=0.9914448613738104,sizingMethod='auto expand')";

             zoom: 1;

Here is a complete example, you just need to play with an angle and translation base on your dimensions.

<div style="background-color: #BCBCBC; width: 100px; height: 50px; padding: 0; margin: 0">
    <div style="width: 112px; height: 47px; border-bottom: 1px solid black; -webkit-transform:   translateY(-20px) translateX(5px) rotate(27deg); "></div>
</div>

You can:

1. create html element (div)
2. set background color to transparent
3. set color to one border
4. rotate