In this note we investigate the length of a strictly descending chain of maximum length in simple groups of Lie type in odd characteristic p. We desire information regarding which maximal subgroups can support (serve as the initial proper step in a longest chain) a longest chain in in G. Considered herein are those M possessing a simple Generalized Fitting subgroup. We show that if M supports a longest chain and has length exceeding that of every maximal parabolic subgroup of G, then either F*(M) is a Lie type group in the same characteristic as C, or Alt(5) = F*(M) = M and G≌L2(p)