An object of the present invention is to provide a cryopreservation vessel which has a coating that is capable of inhibiting the adhesion of cells or proteins and is resistant not only to aqueous solvents but also to organic solvents (for example, cryoprotectants, in particular, dimethyl sulfoxide). The invention provides a cell or protein cryopreservation vessel including, on at least a portion of the surface thereof, a coating that includes a repeating unit containing a group represented by the following formula (a), and a repeating unit containing a group represented by the following formula (b) (wherein Ua1, Ua2, Ua3, Ub1, Ub2, Ub3 and An−; are as defined in the description and the claims)