  The nature of the antiferromagnetic order in the heavy fermion metal
YbRh$_2$Si$_2$, its quantum criticality, and superconductivity, which appears
at low mK temperatures, remain open questions. We report measurements of the
heat capacity over the wide temperature range 180 $\mu$K - 80 mK, using current
sensing noise thermometry. In zero magnetic field we observe a remarkably sharp
heat capacity anomaly at 1.5 mK, which we identify as an electro-nuclear
transition into a state with spatially modulated electronic magnetic order of
maximum amplitude 0.1$\mu_B$. We also report results of measurements in
magnetic fields in the range 0 to 70 mT, applied perpendicular to the c-axis,
which show eventual suppression of this order. These results demonstrate a
coexistence of a large moment antiferromagnet with putative superconductivity.
