Ok, just to be certain. Go to Object mode and select the object that is the upper part of the chair. Combining my method and hihosilver's, go to the Top view and move the entire object so the centre of the seat coincides with the grey central crosshairs. Now, click the button below the select mode arrow button and use the movement tool to move the coloured arrows that represent the object's centre of rotation to also coincide with the central grey crosshairs (you will need to be in wireframe mode to see them). Now, still in the origin mode, click on the select arrow (not select mode) and click on the screen, somewhere where your object isn't so the object deselects while in origin mode (this can be important - without this sometimes the origin does not stay moved). Now you can return to select mode (top left button) and then to scene mode, and the object should rotate about its own centre.
Also, I notice from your images that the chair is rotating wonkily. If you deselect the "Y" and "Z" buttons when rotating, rotation will be constrained to the "X" dimension (left/right in screen coordinate mode, which you are in) and the chair will stay straight.
I hope this helps. If it doesn't make sense (which is a distinct possibility - I have just got out of bed, its Sunday morning, and last night's indulgences are punishing me severely) I will post some screen shots.