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Unconventional superconductivity (USC) in a highly correlated kagome systemhas been theoretically proposed for years, yet the experimental realization ishard to achieve. The recently discovered vanadium-based kagome materials, whichexhibit both superconductivity and charge density wave (CDW) orders, arenonmagnetic and weakly correlated, thus unlikely host USC as theories proposed.Here we report the discovery of a chromium-based kagome bad metal,CsCr$_3$Sb$_5$, which is contrastingly characterised by significant electroncorrelations and frustrated magnetism. Successive phase transitions at $\sim$54K with stripe-like $4a_0$ structural modulations are observed, probablyassociated with CDW and antiferromagnetic spin-density-wave (SDW) orderings.Under moderately high pressures of 4-8 GPa, these density-wave orders aresuppressed and, remarkably, superconductivity emerges with a maximum$T_\mathrm{c}$ of 6.4 K. A quantum critical point at $P_\mathrm{c}\approx$ 4GPa is revealed, by which non-Fermi-liquid behaviours show up, reminiscent ofUSC in iron-based superconductors. The electronic structure calculationsindicate that the electron filling is close to the characteristic flat bands ofthe kagome lattice. Our work offers an unprecedented platform for investigatingthe mechanism of USC in a correlated kagome system.

Superconductivity emerged from density-wave order in a kagome bad metal