I have worked with a few international teams on business projects, and great things can be done across seas :)

I would suggest really clarifying expectations and responsibilities of each position. Would the 4th American guy be amenable to checking in regularly (however you define that) on projects? Are you all comfortable (or willing to become comfortable) with video-chat meetings and emails? Do you already have much of the strategy in place?

Location shouldn't be a problem as long as all of you share similar zeal, passion, vision, and intent to grow the business. But, do take your time to analyze the goodness of fit. I've seen people taking such decision in haste, only to waste the most precious thing a startup possess i.e. time.

To be present in the right market and under the same roof does help you to plan better and practical. Staying at home syndrome could prove fatal down the line and may frustrate everyone in the team. I've seen early entrepreneurs using modern cloud and digital technology as an alibi to justify staying at home syndrome. Ensure you don't make the same mistake. Let me know if I could be of any help to read between and behind the line. All the best!!

Don't see this as a negative its actually a positive. It can be difficult for companies to grow in different countries but having a person there can be really beneficial. Especially when it comes to needed access to US bank accounts or Services. Most of the online Market is in the US, so this is plus's all round. Just be sure his stack is smaller in that you don't have to run past all your decisions with him. Chances are because his a coder he would rather play a more technical role anyway

The most intuitive answer is to say "Global Economy"! "The Internet made as live in one global village so location doesn't matter anymore".
But life is a bit more complicated. You have mentioned that the guy supposed to be your CTO, or basically, your main developer and probably supervising other developers.In that case, some of the points you should consider are: will he need to work closely with others in the company? Will he need to supervise others? Will he be able to perform his duties remotely without supervision?
Don't forget that there is a time difference as well but this could be bridged and not an issue when you schedule a call for early-late afternoon in Europe when in the US we just starting our day. This can be an advantage as well as this way the "Company's working day" is extended.
Which brings me to the next question - Where in the US will he be? East Coast? West Coast? Else?
Will he be in a place where he can do more than programming but also business development and meet with relevant clients/investors/partners?
If you have more questions or want to give more information give me a call to discuss.

I've been in two startups with international teams - technical ones in different countries.

I agree with the other answers here that technology now is superb at helping people keep in touch - e.g www.slack.com - so collaboration is much easier. You need to make sure they're always part of the team and feel involved. I know one company who puts a tv screen in their office and has a live Skype video feed playing at all times so everyone can see each other.

Just be careful about giving them the VP or CTO role though as ultimately that person will be building the tech team and they'll only be able to do that back in the US... so if you're happy with all team being there then that's fine.. else Senior Developer is flexible enough.

What ever you decide - get them either on a contract basis or bring them into the team with equity - but make sure it has a good vesting clause (i.e. they earn shares every 3 months until the agreement is terminated).