Atomic-resolution-imaging approaches for single molecules, such as coherent X-ray diffraction at free-electron lasers, require the delivery of high-density beams of identical molecules. However, even very cold beams of biomolecules typically have multiple conformational states populated. We demonstrate the production of very cold (T-rot approximate to 2.3 K) molecular beams of intact dipeptide molecules, which were then spatially separated into the individual populated conformational states. This is achieved using the combination of supersonic expansion laser-desorption vaporization with electrostatic deflection in strong inhomogeneous fields. This represents the first demonstration of a conformer-separated and rotationally cold molecular beam of a peptide, which enables the investigation of conformer-specific chemistry using inherently non-conformer-specific techniques. It furthermore represents a milestone toward the direct structural imaging of individual biological molecules with atomic resolution by ultrafast diffractive-imaging methods.