We report that Cu9O2(SeO3)(4)Cl-6 is a new multiferroic compound. Comprehensive studies of this compound have been carried out on single crystals as well as polycrystalline samples. Magnetic susceptibility chi and specific heat C with H parallel to c axis both reveal an anomaly at T-N = 37 K associated with the long-range antiferromagnetic order. However, no signature of this phase transition is seen with the H parallel to b axis, providing evidence of the anisotropic nature of its magnetic properties. The results of chi measurements are consistent with the temperature evolution of the intensity of magnetic reflections from the neutron diffraction experiments. The magnetic structure derived from neutron scattering measurements shows that half of the Cu(5) ions carry no moments. Furthermore, an anomaly in the dielectric constant near T-N and observable magnetoelectric coupling below T-N are found. At high temperatures, a dielectric peak at T-E = 267 K is identified with no measurable spontaneous polarization below T-E, thereby suggesting an antiferroelectric order. A steplike anomaly seen in chi(T) at T-E hints the weak spin-lattice coupling. Concomitantly, high-resolution temperature-dependent synchrotron x-ray diffraction experiments elucidate a local structural distortion at T-E.