Is there a CSS selector for the first direct child only?

I have the following html

<div class="section">
   <div>header</div>
   <div>
          contents
          <div>sub contents 1</div>              
          <div>sub contents 2</div>
   </div>
</div>

And the following style:

DIV.section DIV:first-child 
{
  ...
}

For some reason that I don’t understand the style is getting applied to the “sub contents 1” <div> as well as the “header” <div>.

I thought that the selector on the style would only apply to the first direct child of a div with a class called “section”. How can I change the selector to get what I want?