You can use the WordPress Header feature (under the Appearance admin menu “Header”) or you can use a widget in the Showcase widget position by inserting your image into a text widget. For this option, you would just use html code for an image:
To only show this on the front page, you can use what I’ve been using since Encounters and Celestial Reloaded, which is a plugin called Dynamic Widgets. This lets you show widgets on select pages only.
However, if it’s just a single image, you should be able to just use the WordPress Header option instead.