The magnetoelectricity of the boracite Cr3B7O13Cl has been studied by quasi-static and dynamic magnetoelec. (ME)H measurements on (001)cub platelets with a ferroelastic/ferroelec. single domain state, obtained by poling with an elec. field of E - 45 kV.cm-1, applied upon cooling through the 42mL' -> mm21' phase transition at 160 K. The magnetoelec. effect has been found to be essentially quadratic with typical values of the ME tensor components b333 = 1.5 x 10-18 [s/A] and b322 = 4 x 10-19 [s/A] at 4.2 K, whereas the linear ME coeff. a33 shows strangely small and fluctuating values of the order of 5 x 10-14 [s/m]. The temp. dependence of the ME effect has been measured between 1.8 and 40 K, indicating a spread max. of b333 near 11 K. The magnetic torque showed a not completely quadratic dependence vs. magnetic field at 4.2 K, thus suggesting the contribution of weakly ferromagnetic ordering. The information obtained at this stage of study permits one to derive the magnetic symmetry of Cr3B7O13Cl at 4.2 K only tentatively to be the orthorhombic with point group m'm'2, implying a very weak spontaneous magnetization parallel to the twofold polar axis. The temp. dependence of the spontaneous polarization Ps has been investigated down to 4 K. [on SciFinder (R)]