Precise polarization measurements in the vacuum ultraviolet (VUV) region provide a new means for inferring weak magnetic fields in the upper atmosphere of the Sun and stars. We propose a VUV spectropolarimeter design ideally suited for this purpose. This design is proposed and adopted for the NASA-JAXA chromospheric lyman-alpha spectropolarimeter (CLASP), which will record the linear polarization (Stokes Q and U) of the hydrogen Lyman-α line (121.567 nm) profile. The expected degree of polarization is on the order of 0.1%. Our spectropolarimeter has two optically symmetric channels to simultaneously measure orthogonal linear polarization states with a single concave diffraction grating that serves both as the spectral dispersion element and beam splitter. This design has a minimal number of reflective components with a high VUV throughput. Consequently, these design features allow us to minimize the polarization errors caused by possible time variation of the VUV flux during the polarization modulation and by statistical photon noise.