The demographics of dwarf galaxy populations have long been in tension with predictions from the Cold Dark Matter (CDM) paradigm. If primordial density fluctuations were scale-free as predicted, dwarf galaxies should themselves host dark matter subhaloes, the most massive of which may have undergone star formation resulting in dwarf galaxy groups. Ensembles of dwarf galaxies are observed as satellites of more massive galaxies, and there is observational and theoretical evidence to suggest that these satellites at z=0 were captured by the massive host halo as a group. However, the evolution of dwarf galaxies is highly susceptible to environment making these satellite groups imperfect probes of CDM in the low mass regime. We have identified one of the clearest examples to date of hierarchical structure formation at low masses: seven isolated, spectroscopically confirmed groups with only dwarf galaxies as members. Each group hosts 3-5 known members, has a baryonic mass of similar to 4.4 x 10 degrees to 2 x 10(10) (M-circle dot and requires a mass-to-light ratio of <100 to be gravitationally bound. Such groups are predicted to be rare theoretically and found to be rare observationally at the current epoch and thus provide a unique window into the possible formation mechanism of more massive, isolated galaxies.