Is there a video hosting site where I can upload 1080p video in MP4, H264, AAC without it being reencoded, losing quality?

You're not likely to find a service that does this, unless it's just a general file hosting/serving platform. I work at Wistia, and knowing the things that go into serving video--it just doesn't make sense to serve most folks' raw files. There are data rate, compatibility, etc. issues to consider. In addition, there are still a lot of people even just in the US who can't actually stream HD video. Check it out: http://wistia.com/blog/hd-video-data/ If you want to serve that video, my suggestion is to get a simple Amazon S3 account or some similar service (perhaps a public Dropbox folder like mentioned) to just serve the video as is from a server. It won't be pretty for viewers, but at least you'll get it in the state you'd like it. If I had a true recommendation for you, though, it would likely be to use some video editing software to re-encode the video yourself to a place you're happy with–data rate, size, audio quality, etc. that would be a more manageable file size. Of course, I don't know the nature of the video nor do I know other specifics about it–but thinking about the data transfer rate to properly stream it is an important consideration if you want folks to view it.

Option 1 : I would try Wistia. It is fairly expensive but, the streaming is just amazing. http://Mixergy.com uses Wistia for all of it's videos. Option 2 : You can use Amazon AWS server to host your file and use Easy Video Player (http://easyvideoplayer.com/evp-2.0/) or Flowplayer to stream those videos. Option 3 : Vimeo Pro (http://vimeo.com/pro). As far as I know Vimeo Pro ( not to be mistaken with VImeo Plus) has a very good lossless HD streaming. But not 100% sure if it uses any different technology than the VImeo & Vimeo Plus. Hope that helps.