Very massive stars, 100 times heavier than the sun, are rare. It is not yet known whether such stars can form in isolation or only in star clusters. The answer to this question is of fundamental importance. The central region of our Galaxy is ideal for investigating very massive stars and clusters located in the same environment. We used archival infrared images to investigate the surroundings of apparently isolated massive stars presently known in the Galactic Center. We find that two such isolated massive stars display apparent bow shocks and hence may be runaways from their birthplace. Thus, some isolated massive stars in the Galactic Center region might have been born in star clusters known in this region. However, no bow shock is detected around the isolated star WR102ka (Peony nebula star), which is one of the most massive and luminous stars in the Galaxy. This star is located at the center of an associated dusty circumstellar nebula. To study whether a star cluster may be hidden in the surroundings of WR102ka, to obtain new and better spectra of this star, and to measure its radial velocity, we obtained observations with the integral-field spectrograph SINFONI at the ESOs Very Large Telescope (VLT). Our observations confirm that WR102ka is one of the most massive stars in the Galaxy and reveal that this star is not associated with a star cluster. We suggest that WR102ka has been born in relative isolation, outside of any massive star cluster.