We present design and performance of a scanning tunneling microscope (STM) that operates at temperatures down to 10 mK providing ultimate energy resolution on the atomic scale. The STM is attached to a dilution refrigerator with direct access to an ultra high vacuum chamber allowing in situ sample preparation. High magnetic fields of up to 14 T perpendicular and up to 0.5 T parallel to the sample surface can be applied. Temperature sensors mounted directly at the tip and sample position verified the base temperature within a small error margin. Using a superconducting Al tip and a metallic Cu(111) sample, we determined an effective temperature of 38 +/- 1 mK from the thermal broadening observed in the tunneling spectra. This results in an upper limit for the energy resolution of Delta E = 3.5k(B)T = 11.4 +/- 0.3 mu eV. The stability between tip and sample is 4 pm at a temperature of 15 mK as demonstrated by topography measurements on a Cu(111) surface. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4793793]