The purpose of the present invention is to attain optimal gas exchange, nutrient supply and disposal of metabolic waste products without contamination during high-density cell cultivation of adherent cells. The culture vessel of the present invention provides methods and apparatus for the cultivation of cells on a three-dimensional carrier in a closed cell culture chamber, the supply with oxygen taking place across a gas-permeable gas exchange membrane bordering the cell culture chamber and the supply with nutrients taking place across a dialysis membrane bordering the cell culture chamber, across which nutrients are transported and across which metabolic products are removed, without the danger of contaminating the cells during contact with the tools necessary for manually separating the cells being cultivated from the nutrient medium. The cell culture chamber of the present invention features a vessel that is impermeable to fluids on all sides except for the boundary formed by the dialysis membrane. This makes it possible to move the cell culture intensively within a fluid nutrient supply medium. It is neither necessary to open the cell culture chamber during cultivation to introduce new nutrients, nor is it necessary for the design to include components which reach into the cell culture chamber, and form an additional source of contamination. The gas exchange membrane is detachable to allow removal of the cultivated cells in a uniform layer on the carrier, and the carrier is bio-degradable to eliminate the need to remove the cells from the carrier prior to use, such as in the transplantation of skin for example.