In this paper, we present a novel grasp selection algorithm to enable a robot with a two-fingered end-effector to autonomously grasp unknown objects. Our approach requires as input only the raw depth data obtained from a single frame of a 3D sensor. Additionally, our approach uses no explicit models of the objects and does not require a training phase. We use the grasping capability to demonstrate the application of a robot as an autonomous checkout clerk. To perform this task, the robot must identify how to grasp an object, locate the barcode on the object, and read the numeric code. We evaluate our grasping algorithm in experiments where the robot was required to autonomously grasp unknown objects. The robot achieved a success of 91.6% in grasping novel objects. We performed two sets of experiments to evaluate the checkout robot application. In the first set, the objects were placed in many orientations in front of the robot one at a time. In the second set, the objects were placed several at a time with varying amounts of clutter. The robot was able to autonomously grasp and scan the objects in 49/50 of the single-object trials and 46/50 of the cluttered trials.