Image guidance promises to improve targeting accuracy and broaden the scope of medical procedures performed with needles. This paper takes a step toward automating the guidance of a flexible tip-steerable needle as it is inserted into the human tissue. We build upon a previously proposed nonholonomic model of needles that derive steering from asymmetric bevel forces at the tip. The bevel-tip needle is inserted and rotated at its base in order to steer it in 6 DOF. As a first step for control, we show that the needle tip can be automatically guided to a planar slice of the tissue as it is inserted. Our approach keeps the physician in the loop to control insertion speed. The distance of the needle tip position from the plane of interest is used to drive an observer-based feedback controller that we prove is locally asymptotically stable. Numerical simulations demonstrate a large domain of attraction and robustness of the controller in the face of parametric uncertainty and measurement noise. Physical experiments with tip-steerable nitinol needles inserted into a transparent plastisol tissue phantom under stereo image guidance validate the effectiveness of our approach.