"choose either" is correct and usable in written English.
You would use it to indicate that someone has two options to choose from. For example: You must choose either beef or chicken for the main course.
The tied athletes must independently choose either a) a coin toss or b) a runoff – or decline to choose either one.
Near-starvation and castration both bring unusual longevity, but few of us choose either option.
Since the difference is trivial we may choose either way, but a decision must be made".
Each opportunity for choice is an opportunity to choose either well or poorly.
On PlayStation, just hit the share button, choose either Twitch or Ustream, then you're off.
You may choose either of two explanations.
If you cannot choose either way, come to Mungyeong.
The participants were able to choose either language.
Surgeons can choose either method according to different clinical needs.
For unbounded variable we can choose either normal or log-normal distribution.
