can i chain from my hand if it is my turn???

example:
i summon lets say blue eyes and my opponent chains with bottomless trap hole. i was wondering if i could chain that with book of moon from my hand???

Yes, during your turn, you can chain quick-play Spell Cards from your hand.

From Netrep


If the opponent Summons a monster, then you activate "Bottomless Trap Hole", and the opponent chains "Book of Moon" to flip the Summoned monster face-down, it is not removed from play by the effect of "Bottomless Trap Hole".

So, you CAN use Book of Moon to prevent your mon from being removed from play. Keep in mind that you WON'T be able to flip it back into ATK position during that turn since by summoning it face up ATK in the first place, you chose its battle position for that turn.

Also, keep in mind, that you nor the opponent can chain to a summon.