While hooks and filters are good to know (I struggle), you are probably just wanting to utilize some CSS.
It looks as if your sidebar won't be terribly complicated, if that is the case, try just moving the sidebar up on top of the header with a negative top margin.
Change existing or add this to your CSS file..
This part moves the sidebar up into the header area.
#primary { margin-top: -100px; }
Now you may notice your sidebar goes underneath the header, that is because of a z-index that is set by default (not sure why, drop downs?). So this will reset that.
#header { z-index: auto; }
Now it is still going to be hidden behind the main div, the reason is it is set to overflow:hidden. Now this only really comes into play as far as I know for clearing background images that repeat and is never necessary. So modify that too.
#main { overflow: inherit; }
This will be much easier than adding a new div, but still learn those hooks and filters. ;)