Teleoperation is widely used in human-hostile or otherwise inaccessible environments. However, using teleoperation to perform a task is more difficult than performing the task directly. A main factor for this is limited telepresence due to the absence or distortion of natural sensory feedback. An interesting possibility to increase telepresence and enhance teleoperation performance is inducing a Body Illusion which may give human operators the sensation that the remote tool belongs to their own body. This study investigated the possibility of inducing the Projected Hand Illusion during a teleoperated reaching task, and its effects on accuracy. The participants (n=16) reached for targets while avoiding stationary obstacles, by manipulating a master device coupled to a slave device. Three conditions were randomly presented: the Direct Control (DC) condition, showing the master device with the participants' own hand, the Projected Hand Illusion (PHI) condition, showing the slave device consisting of a 3D-printed hand designed to induce a Body Illusion, and the no Projected Hand Illusion (nPHI) condition, showing the slave device consisting of a 3D-printed object of similar shape designed to not induce a Body Illusion. A questionnaire was used to assess the subjective feeling of the Projected Hand Illusion. Based on the questionnaire responses, participants were grouped in the qualifying group (n=5) or the non-qualifying group (n=11). It was found that the Projected Hand Illusion was consistently induced in both conditions, and for both groups. Also, a significant difference in distance to target in the y-direction and x-direction was found between conditions PHI and nPHI; in the nPHI condition, participants kept more distance to the obstacle than in the PHI condition. This may suggest an increased perception of risk due to a difference in visual perception or due to the Body Illusion. However, as the Body Illusion was present in both conditions according to the metric used, and the differences between conditions were found for both groups, these findings cannot be attributed to the presence of the Body Illusion with certainty. Therefore, more in-depth studies investigating the possible causes are recommended. This research shows that a Body Illusion can be evoked during teleoperation, and possibly affect its performance. Therefore, this exploratory study gives rise to further research into the practical application of Body Illusions in teleoperation.