  When measuring electromagnetic radiation of frequency $f$, the most sensitive
detector is the one that counts the single quanta of energy $h f$. Single
photon detectors (SPDs) were demonstrated from $\gamma$-rays to infrared
wavelengths, and extending this range down to the microwaves is the focus of
intense research. The energy of $10\,\mathrm{GHz}$ microwave photon, about
$40\,\mathrm{\mu eV}$ or $7\, \mathrm{yJ},$ is enough to force a
superconducting Josephson junction into its resistive state, making it suitable
to be used as a sensor. In this work, we use an underdamped Josephson junction
to detect single thermal photons stochastically emitted by a microwave copper
cavity at millikelvin temperatures. After characterizing the source and
detector, we vary the temperature of the resonant cavity and measure the
increased photon rate. The device shows an efficiency up to 40% and a dark
count rate of $0.1\,\mathrm{Hz}$ in a bandwidth of several gigahertz. To
confirm the thermal nature of the emitted photons we verify their
super-Poissonian statistics, which is also a signature of quantum chaos. We
discuss detector application in the scope of Dark Matter Axion searches, and
note its importance for quantum information, metrology and fundamental physics.
