Hierarchical graphene architectures (HGAs) that grow by stacking of layers are produced on a liquid copper surface using chemical vapor deposition. The stacking mode - for example hexagonal-hexagonal-hexagonal or hexagonal-snowflake-dendritic - can be simply controlled. Measurements of the electrical properties of HGAs indicate that hierarchical stacking of graphene may be a simple and effective way of tailoring their properties without degrading them.