Accurate knowledge of the thermal conductivities of biological tissues is important for thermal bioengineering, including applications in cryopreservation, cryosurgery, and other thermal therapies. The thermal conductivity of biomaterials is traditionally measured with macroscale techniques such as the steady longitudinal heat flow method or embedded thermistor method. These techniques typically require relatively large, centimeter-scale samples, limiting their applicability to finer biological structures. They are also vulnerable to errors caused by thermal contact resistances and parasitic heat losses. In contrast, the thermal conductivity of inorganic solids such as semiconductor wafers and thin films is commonly measured using the "3 omega method" [1-3]. This frequency domain technique is robust against thermal contact resistances and parasitic heat losses. It routinely has sub-millimeter spatial resolution, with theoretical limits down to tens of microns. Here we adapt the 3 omega method for measurements of biological tissues. Thermal conductivity measurements are made on both frozen and un-frozen samples including agar gel, water, and mouse liver, including samples with sub-millimeter thicknesses. The measurement results compare favorably with literature values and span the range from around 0.5 to 2.5 W/m-K. This study demonstrates the promise that this technique holds for thermal measurements of bulk tissues as well as fine sub-millimeter samples.