From Webster's Revised Unabridged Dictionary (1913):
Hegemony \He*gem`o*ny\, n. [Gr. ?, fr. ? guide, leader, fr. ? to go before.] Leadership; preponderant influence or authority; -- usually applied to the relation of a government or state to its neighbors or confederates. --Lieber.
(note from jonez: thanks to tmojd for telling me about this cool word, thanks to a certain friend for acting this way which inspired tmojd to tell me about this word, and thanks to dict.org for keeping the big database that I cut and pasted the above definition from)