As a US citizen entering the UK with a Tier 4 Visa, do I need to have a chest x-ray before hand?
Not if you are applying in the USA! And that is not based upon your nationality, but where you are applying.
That is, if you, a USC are currently living in say Thailand, and you intend to apply for your visa in Bangkok, yes you would need to have a TB examination prior to applying for your visa ..... because Thailand is on the list requiring that.
Conversely, if a Thai citizen is currently living legally in the US, and now want to apply for a UK visa, applying in the US, they would not require a TB examination.