box-shadow on top of children

To avoid the use of an additional element, you can use css pseudo-elements. Try this demo.

#chatroom {
    position: relative;
}

#chatroom:before {
    content: "";

    /* Expand element */
    position: absolute;
    left: 0px;
    top: 0px;
    right: 0px;
    bottom: 0px;

    -moz-box-shadow: inset 0 0 8px rgba(0,0,0,.55);
    -webkit-box-shadow: inset 0 0 8px rgba(0,0,0,.55);
    box-shadow: inset 0 0 8px rgba(0,0,0,.55);

    /* Disable click events */
    pointer-events: none;
}

Basically this css creates that additional element for you. Notice the pointer-events:none to allow click events to pass through this element.

Keep in mind that pointer-events:none doesn't work well on some mobile devices regarding touch scrolling (clicking/taping works well). I ended up not using inset shadows at all because of this.

cant be done directly from css.. (it is not shadow if it goes above overlapping elements)

you would need to rework your html a bit by adding a div (or use a pseudo element as suggested by miguelcobain's answer) to overlay the shadow and your CSS to make the new div have the shadow..

#chatroom {
  border: 1px solid #CCC;
  height: 135px;
  font-size: 0.75em;
  line-height: 1.2em;
  overflow: auto;
  position: relative;
}

.shadow {
  position: absolute;
  left: 0px;
  top: 0px;
  right: 0px;
  bottom: 0px;
  -moz-box-shadow: inset 0 0px 4px rgba(0, 0, 0, .55);
  -webkit-box-shadow: inset 0 0px 4px rgba(0, 0, 0, .55);
  box-shadow: inset 0 0px 4px rgba(0, 0, 0, .55);
}

.chatmessage {
  padding: 4px 2px;
}

.chatmessage b {
  margin-right: 2px;
}

.chatmessage:nth-child(2n) {
  background: #EEE;
}

<div id="chatroom">
  <div class="chatmessage"><b>User 1:</b>Test</div>
  <div class="chatmessage"><b>User 2:</b>Test</div>
  <div class="chatmessage"><b>User 1:</b>Test</div>
  <div class="chatmessage"><b>User 2:</b>Test</div>
  <div class="shadow"></div>
</div>