A bijective function $f:V\rightarrow\left\{1,2,3,...,|V| \right\}$ is said to be a local distance antimagic labeling of a graph $G=(V,E)$, if $w(u)\neq w(v)$ for any two adjacent vertices $u, v$ where the weight $w(v)=\sum_{z\in N(v)}f(z)$. The local distance antimagic labeling of $G$ induces a proper coloring in $G$, called local distance antimagic chromatic number denoted by $χ_{ld}(G)$. In this article, we introduce the parameter $χ_{ld}(G)$ and compute the local distance antimagic chromatic number of graphs. Keywords: Distance antimagic labeling, Local distance antimagic labeling, Local distance antimagic chromatic number.