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Generalising the chiral boundary conditions of $\mathbb{R}^{1,3}$ gravity forAdS$_4$ gravity, we derive chiral locally AdS$_4$ solutions in the Newman-Untigauge consistent with a variational principle whose asymptotic symmetry algebrawe show, to be an infinite-dimensional chiral extension of$\mathfrak{so}(2,3)$. This symmetry algebra coincides with the chiral$\mathfrak{bms}_4$ algebra in the flat space limit. We posit this symmetryalgebra as the chiral version of recently discovered$\Lambda$-$\mathfrak{bms}_4$ algebra. We postulate line integral charges fromthe bulk AdS$_4$ gravity corresponding to this chiral symmetry algebra and showthat the charges obey the semi-classical limit of a $\mathcal{W}$-algebra thatincludes a level $\kappa$ Kac-Moody $\mathfrak{sl}(2,\mathbb{R})$ currentalgebra. Furthermore, using the standard tools of $2d$ CFT, we derive thequantum version of this $\mathcal{W}$-algebra which may be denoted by$\mathcal{W}(2;(3/2)^2,1^3)$.

A Chiral ${\Lambda}$-$\mathfrak{bms}_4$ Symmetry of AdS$_4$ Gravity