  We describe the design, construction, and performance of an ultra-low
temperature, high-field scanning tunneling microscope (STM) with two
independent tips. The STM is mounted on a dilution refrigerator and operates at
a base temperature of 30 mK with magnetic fields of up to 13.5 T. We focus on
the design of the two-tip STM head, as well as the sample transfer mechanism,
which allows \textit{in situ} transfer from an ultra high vacuum (UHV)
preparation chamber while the STM is at 1.5 K. Other design details such as the
vibration isolation and rf-filtered wiring are also described. Their
effectiveness is demonstrated via spectral current noise characteristics and
the root mean square roughness of atomic resolution images. The high-field
capability is shown by the magnetic field dependence of the superconducting gap
of $\text{Cu}_x\text{Bi}_2\text{Se}_3$. Finally, we present images and
spectroscopy taken with superconducting Nb tips with the refrigerator at 35 mK
that indicate that the effective temperature of our tips/sample is
approximately 184 mK, corresponding to an energy resolution of 16 $\mu$eV.
