By prior work, there is a distributed graph algorithm that finds a maximal fractional matching (maximal edge packing) in $$O(\varDelta )$$ O ( Δ ) rounds, independently of $$n$$ n ; here $$\varDelta $$ Δ is the maximum degree of the graph and $$n$$ n is the number of nodes in the graph. We show that this is optimal: there is no distributed algorithm that finds a maximal fractional matching in $$o(\varDelta )$$ o ( Δ ) rounds, independently of $$n$$ n . Our work gives the first linear-in- $$\varDelta $$ Δ lower bound for a natural graph problem in the standard $$\mathsf{LOCAL }$$ LOCAL model of distributed computing—prior lower bounds for a wide range of graph problems have been at best logarithmic in $$\varDelta $$ Δ .