Your answer depends on a lot of factors...
1) the palyer chasing (is he a donk, solid, aggressive)? If he is a donk, there is nothing really you can do. chances are if you don't bet, he's goin all-inanyway. If he is a solid player then you have to make it not worth his while by aggrtessively betting. that tactic may or may not work for the aggreesive player.
2) the event - freerolls
? fugetabotit! they will chase no matter what and they will catch. Dont get mad, just think they freed up some time for you if they bust you out. Freerolls are a sort of bizarro land in the poker world. I only play it to laugh at the other players who take it serious. Ring games and cashy tournaments have a more savy player but beware of the first hour where donks abound 4:1 (wow same odds as the dlush draw. (have fun)