  Non-reciprocal electronic transport in a material occurs if both time
reversal and inversion symmetries are broken. The superconducting diode effect
(SDE) is an exotic manifestation of this type of behavior where the critical
current for positive and negative currents are mismatched, as recently observed
in some non-centrosymmetric superconductors with a magnetic field. Here, we
demonstrate a SDE in non-magnetic Nb/Ru/Sr$_2$RuO$_4$ Josephson junctions
without applying an external magnetic field. The cooling history dependence of
the SDE suggests that time-reversal symmetry is intrinsically broken by the
superconducting phase of Sr$_2$RuO$_4$. Applied magnetic fields modify the SDE
dynamically by randomly changing the sign of the non-reciprocity. We propose a
model for such a topological junction with a conventional superconductor
surrounded by a chiral superconductor with broken time reversal symmetry.
