Abstract: An L(3,2,1)-labeling of a graph G is a function from the vertex set V(G) to the set of all nonnegative integers such that |f(u)-f(v)|> 3 if d_G(u,v)=1,|f(u)-f(v)|> 2 if d_G(u,v)=2, and |f(u)-f(v)|> 1, if d_G(u,v)=3. The L(3,2,1)-labeling problem is to find the smallest number _3(G) such that there exists an L(3,2,1)-labeling function with no label greater than it. In this paper, we study this problem for chordal graphs. We obtain bounds of \lambda_3 number for chordal graphs and its subclasses, such as fan, r-path, r-tree and so on.