  We construct a novel charged Taub-NUT spacetime, providing a first
non-trivial example of a self-gravitating solution to the recently proposed
ModMax theory, the most general (1-parametric) theory of non-linear
electrodynamics that is characterized by both the conformal symmetry and the
$SO(2)$ duality-rotation invariance. The spacetime features non-trivial
magnetic fields, in their presence the non-linearity of the field becomes
apparent and the solution is distinguished from that of the Maxwell theory.
Thermodynamics of the new solution, the charged black hole limit of vanishing
NUT parameter, and the self-dual solutions are also briefly discussed.
