  The role of nematic order for the mechanism of high-temperature
superconductivity is highly debated. In most iron-based superconductors (IBS)
the tetragonal symmetry is broken already in the normal state, resulting in
orthorhombic lattice distortions, static stripe magnetic order, or both.
Superconductivity then emerges, at least at weak doping, already from the state
with broken $C_4$ rotational symmetry. One of the few stoichiometric IBS,
lithium iron arsenide, superconducts below 18 K and does not display either
structural or magnetic transition in the normal state. Here we demonstrate,
using angle-resolved photoemission, that even superconducting state in LiFeAs
is also a nematic one. We observe spontaneous breaking of the rotational
symmetry in the gap amplitude on all Fermi surfaces, as well as unidirectional
distortion of the Fermi pockets. Remarkably, these deformations disappear above
superconducting $T_c$. Our results demonstrate the realization of a novel
phenomenon of superconductivity-induced nematicity in IBS, emphasizing the
intimate relation between them. We suggest a theoretical explanation based on
the emergence of a secondary instability inside the superconducting state,
which leads to the nematic order and s-d mixing in the gap function.
