A proper coloring c : V (G) → {1, 2, . . . , k}, k ≥ 2 of a graph G is called a graceful k-coloring if the induced edge coloring c ′ : E(G) → {1, 2, . . . , k − 1} defined by c ′ (uv) = |c(u) − c(v)| for each edge uv of G is also proper. The minimum integer k for which G has a graceful k-coloring is the graceful chromatic number χg(G). It is known that if T is a tree with maximum degree ∆, then χg(T ) ≤ ⌈ 5⁄3∆⌉ and this bound is best possible. It is shown for each integer ∆ ≥ 2 that there is an infinite class of trees T with maximum degree ∆ such that χg(T ) = ⌈ 5⁄3 ∆⌉. In particular, we investigate for each integer ∆ ≥ 2 a class of rooted trees T∆,h with maximum degree ∆ and height h. The graceful chromatic number of T∆,h is determined for each integer ∆ ≥ 2 when 1 ≤ h ≤ 4. Furthermore, it is shown for each ∆ ≥ 2 that lim h→∞ χg(T∆,h) = ⌈ 5⁄3∆⌉.