Amber has been appreciated by mankind for its color and natural beauty since the Neolithic era. However, amber can also be a gemstone for physics and chemistry research on glasses. In this work, we have measured the specific heat of 110 million-year-old Spanish amber to temperatures below 0.1 K, and show that the two most prominent and ubiquitous features of glasses at low temperatures, namely the presence of tunneling two-level systems and the so-called boson peak, persist essentially unchanged in highly stabilized glasses, contrary to what was usually envisaged during last forty years. Therefore, these controversial features of all non-crystalline solids at low temperatures are shown to be indeed robust and intrinsic properties which also remain “fossilized” in 110-million-year aged glasses of Spanish amber, as insects or other bioinclusions do. We expect that amber will serve in the near future as an extremely enlightening model glass to study many other puzzles involved in the physics of the glass state.