Let G be a connected simple graph with the vertex set $V\left(G\right)=\{v_1,v_2,\dots ,v_n\}$, where the distance $d_G(v_i,v_j)$ is the length of a shortest path between $v_i$ and $v_j$, and the distance matrix $D\left(G\right)=\left(d_{ij}\right)n\times n$ is defined by $d_{ij}=d_G(v_i,v_j)$. Being real symmetric and non-negative, $D\left(G\right)$ has real eigenvalues ${\lambda }_1\left(G\right)\ge {\lambda }_2\left(G\right)\ge \dots \ge {\lambda }_n\left(G\right)$, with ${\lambda }_n\left(G\right)$ referred to as the least distance eigenvalue of G. In this paper, we give the maximum value of the least distance eigenvalue, and determine the unique extremal graph with two pendant vertices whose complements attain the value.