What version of Zen? And is this a background image, or just an image in the header?
For a fixed width theme, you can insert a background image into the #header with the following CSS:
margin: 0px 0 0 0;
background: transparent url(images/header.png) no-repeat top center;
The Zen 5 markup is a little leaner, and you probably have to add a #header-bgimg div in your page.tpl.php file just inside the regular #header div. Then you can add a header image like this:
padding-top: 33.3%; /* Responsive Scaling: 333px/1000px = 0.3333 */
This time I used additional directives to make it a responsive header image. If you don't use the additional wrapper, you collide with some of the Zen 5 CSS.
Placing other objects in your header might require a #header-inner wrapper just inside the #header-bgimg div.