  We demonstrate a monolithic optical whispering gallery mode resonator
fabricated with barium fluoride (BaF$_2$) with an ultra-high quality ($Q$)
factor above $10^9$ at $1550$ nm, and measured with both the linewidth and
cavity-ring-down methods. Vertical scanning optical profilometry shows that the
root mean square surface roughness of $2$ nm is achieved for our mm-size disk.
To the best of our knowledge, we show for the first time that one billion
$Q$-factor is achievable by precision polishing in relatively soft crystals
with mohs hardness of ~$3$. We show that complex thermo-optical dynamics can
take place in these resonators. Beside usual applications in nonlinear optics
and microwave photonics, high energy particle scintillation detection utilizing
monolithic BaF$_2$ resonators potentially becomes feasible.
