We present the electronic properties of a triple quantum dot molecule embedded inside a sub-micron mesa, made from a quadruple-barrier triplequantum- well structure, and surrounded by a single gate electrode. We outline the design principles of the quadruple-barrier triple-quantum-well structure and calculate the energy of the three lowest states as a function of center well thickness. We observe regular and irregular shaped Coulomb diamond regions similar to those for double quantum dot devices. Variation in the Coulomb blockade region shape is introduced by fluctuation in the offset energies between the quantum dots likely associated with device processing and random impurity potential in the material. We also present Coulomb blockade patterns calculated with a constant interaction model for sequential tunneling through the three series-coupled quantum dots.