Soft X-ray microscopy employs the photoelectric absorption contrast between water and protein in the 2.34-4.38 nm wavelength region to visualize protein structures down to 30 nm size without any staining methods. Due to the large depth of focus of the Fresnel zone plates used as X-ray objectives, computed tomography based on the X-ray microscopic images can be used to reconstruct the local linear absorption coefficient inside the three-dimensional specimen volume. High-resolution X-ray images require a high specimen radiation dose, and a series of images taken at different viewing angles is needed for computed tomography. Therefore, cryo microscopy is necessary to preserve the structural integrity of hydrated biological specimens during image acquisition. The cryo transmission X-ray microscope at the electron storage ring BESSY I (Berlin) was used to obtain a tilt series of images of the frozen-hydrated green alga Chlamydomonas reinhardtii. The living specimens were inserted into borosilicate glass capillaries and, in this first experiment, rapidly cooled by plunging into liquid nitrogen. The capillary specimen holders allow image acquisition over the full angular range of 180 degrees. The reconstruction shows for the first time details down to 60 nm size inside a frozen-hydrated biological specimen and conveys a clear impression of the internal structures. This technique is expected to be applicable to a wide range of biological specimens, such as the cell nucleus. It offers the possibility of imaging the three-dimensional structure of hydrated biological specimens close to their natural living state.