One of the key systematic effects limiting the performance of state-of-the-art optical clocks is the blackbody radiation (BBR) shift. Here, we demonstrate unusually low sensitivity of a 1.14 μm inner-shell clock transition in neutral Tm atoms to BBR. By direct polarizability measurements, we infer a differential polarizability of the clock levels of −0.063(30) atomic units corresponding to a fractional frequency BBR shift of only 2.3(1.1) × 10
−18
at room temperature. This amount is several orders of magnitude smaller than that of the best optical clocks using neutral atoms (Sr, Yb, Hg) and is competitive with that of ion optical clocks (Al
+
, Lu
+
). Our results allow the development of lanthanide-based optical clocks with a relative uncertainty at the 10
−17
level.