In my current campaign, my players are wanting to go investigate why some Gith that they fought are coming from the Astral Plane. So I have set up a mini story and I hope they my players will enjoy it. However there is something that I really badly want to do but it might totally ruin the game. My ultimate BBEG is Asmodeus, and the Gith were recieving instruction from Asmodeus. How they were recieving instruction, via the book of vile darkness. The book will have all the classic really bad things, but I have made it to where it is currently owned by Asmodeus, and making part of the book be like Tom Riddles Diary of Harry Potter and the Chamber of Secrets fame. The Gith leader would read the book and be able to give out instructions for what to do. NOW, with all that said, my players vanquished the Gith army a little while earlier. So when exploring this tower I really want them to get some sort of idea of why the Gith came while hinting at who the BBEG is. SO I really want to put the book of vile darkness in there. (BTW the players would not own this book, they currently have an NPC from Candlekeep with them, and they owe a tome, so she would take that if the party is agreeable. If not then I will see what I can do.) After that the NPC would take the book and the party with the NPC, would travel back to Candlekeep, and learn some of the books ideas, while watching what happens when attuned. But here is the rub, the players are level 3.

tl:dr I really want to put the book of vile darkness in my campaign, because thematically it would advance the campaign alot and give the players more ideas. However they are level 3 and I want to seriously consider what it would mean to put a artifact in my campaign. Any opinions?

If you've got a traditionally heroic party, I think it's fairly safe to let them see the Book of Vile Darkness. There's no way to use it without becoming corrupted in some way, and the benefits all come with a fairly steep cost that's generally out of the range of a level 3 party. However, if you think that any one of your players is power-gamey enough to sacrifice characterization for just a straight power boost, I'd say maybe hold off on giving them the actual book and maybe just have some pages from the book instead. 

I would say go for it. Remember, you are the DM. You control everything. The Book of Vile Darkness could turn out to be a list of really bad dark chocolate recipes. 

My point being that I wouldn't worry about the consequences if you open yourself up to the fact that it can't happen if you don't want it to. If you want to be extra cautious, then maybe don't specify the book exactly until after you NPC has it. If they refuse to give it to her, then this could turn out to be some other, mostly harmless evil tome. Or it could be the exact book of vile darkness, except in your campaign all the pages are blank and thus the book is inert until the command word Suedomas is spoken, but it'll take your NPC some time to study the book to figure that out so she really needs it. 

You're the DM and the plot doesn't move without you. Revel in that power. I know I do!

Let them have the book. Bilbo can't have been much more than level 2 when he found the One Ring, and the storytelling effects from it worked out. But be aware that the whole campaign will need to revolve around it!

I agree with this caveat: IF they decide to keep it and use it, you'd better have some contingency plans laid out or your campaign will blow up on you.

Level 3 is awful early if you're expecting this campaign to go a while. Expanding the scope of your campaign from local to regional to national to global and/or extraplanar (and expanding items and enemies to match) can provide some really good story payoff with each hop and I'm typically hesitant to do it too soon unless it's a short campaign. But it sounds like that ship has sailed.

Personally, I'd still have an evil book but it's not the BoVD. It could still pose similar threats and temptations, perhaps scaled down a bit, and your NPC could identify that many of its passages seem to be copied from the BoVD itself. This teases the idea so that you can set up an encounter later with the real BoVD.

While I keep the scale small at lower levels, I still keep the characters aware that there is a bigger world out there with scary stuff out there. Stuff that would steamroll them as they are currently. I feel like taking the Book of Vile Darkness out of the hands of direct underlings of Asmodeus at level 3 might give the impression that the party can take on pretty much anyone. Which may or may not be what you're going for.

perhaps the room has scattered/torn pages from the BoVD? 

Maybe give them an incomplete copy of the book someone tried to make to secretly gain power for himself and went mad over it. That way, you can limit its powers, while giving any foreshadowing clues you want the players to have, while playing with some horror elements.

Maybe include that lich lady that orders the githyanki around. I forget her name, but she's evil. Maybe make her the BBEG they fight, and Asmodeus the background BBEG (he is a god, so I don't know how high level the party is going to be.)