  All quantum optomechanics experiments to date operate at cryogenic
temperatures, imposing severe technical challenges and fundamental constraints.
Here we present a novel design of on-chip mechanical resonators which exhibit
fundamental modes with frequencies $f$ and mechanical quality factors
$Q_\mathrm{m}$ sufficient to enter the optomechanical quantum regime at room
temperature. We overcome previous limitations by designing ultrathin,
high-stress silicon nitride (Si$_3$N$_4$) membranes, with tensile stress in the
resonators' clamps close to the ultimate yield strength of the material. By
patterning a photonic crystal on the SiN membranes, we observe reflectivities
greater than 99%. These on-chip resonators have remarkably low mechanical
dissipation, with $Q_\mathrm{m}$$\sim$$10^8$, while at the same time exhibiting
large reflectivities. This makes them a unique platform for experiments towards
the observation of massive quantum behavior at room temperature.
