Interesting question...

I go palm towards the floor, myself. What's the consensus like at your gym?

well the hook is the hardest to learn!! and the hardest to throw i've split my traning up by enrolling in the boxing guy in my state.just so i can train my boxing with just boxers and not just muay thai guys..the boxer use a palm down and a slight 45 downward in the arm.i like this way it's more inline with the bone and the shoulder.but i've seen it used all types of way i guess what work the best for you just use it.
Good Luck.

my gym insists on thumb up -- better knuckle contact and reduced risk of injury, if one comes out a little sloppy. the pain i felt after throwing a few palm down sans wraps when i was first starting out would seem to back this up.

i have long debated this to myself, and find either way pretty natural to me altho if a preference is needed i would go with the palm inward method, in my opinion it makes the fist cross the jawline making for a more concussive shot...BAM! take that lol

I agree that the palm should be facing you, but there is a simple way to look at the issue. Your hook is typically used, or at least best, after you or your opponent has slipped a cross. Your "free" hand should be at your head to block your face/head and your elbow should be down to protect the body, your hips should be rotated with your cross and you on your back leg ball of foot. The most natural, fastest, most powerful hook will come from you raising your elbow to level with your shoulder and fist while rotating your hips back as you return your fist used for the cross. The extra motion to rotate your wrist to make your palm down is wasted at best when the hook is applied in this manner and purpose, but it will also force your fist away from you in some cases. Everyone has an opinion on this and there are times when each manner work best. Good luck debating!

when i teach it , i teach palm facing u, thumb up like your holding a beer mug. This keeps bones in line, you can naturally strike with the correct knuckles, and u have less chance at injuing ur wrist. But I do admit when im in the middle of a sparring match i catch myself throwing hooks with my palm down( especially if there longer range hooks) It just seems to fire off more naturally that way.

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Master Lee describes nine ways to throw a hook in his book The Tao of Jeet Kune Do.

the truth is, both ways work fairly well - They have subtly different charecteristics though so one way or another will often fight one's style better. Palm facing yer face is a bit safer for the knuckles, but it gives up range. Some people feel that palm in is faster, some like palm down for the "pop" - I think I do both, depending on "feel"