Great Soviet mathematician [N.I. Akhiezer][1] mentions in his survey article  *"Чебышевское направление в теории функций"* (*"Function Theory According to Chebyshev"*) that the notation
$$T_n(x)=\frac{1}{2^{n-1}} \cos{(n\arccos x)}$$
was first introduced by S. Bernstein. 

I think that the first published paper on the Chebyshev polynomials by Bernstein was *"О наилучшем приближении непрерывных функций посредством полиномов данной степени"* which appeared in "Сообщения Харьковского математического общества", series 2, vol. 13 (**1912**), pp. 49-194. The paper is in Russian as you may guess.

In his paper, Bernstein refers to the Chebyshev polynomials as *trigonometric polynomials* which  probably might explain the letter *T* in the notation.



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English translation of Akhiezer's survey article is contained in [*Mathematics of the 19th Century*][2] edited by A.N. Kolmogorov. 


**Edit added.** I don't know if there is an English translation of the original paper by Bernstein. [This source][3] refers to the paper as *"The optimum approximation to continuous functions by polynomials of a given power"*, Reports of the Kharkov Mathematical Society, Second Series, 1912, 13, #2-3.  The original paper can be also found in volume 1 of S.N. Bernstein Collected Works (*С.Н. Бернштейн, Собрание сочинений (Том 1. Конструктивная теория функций [1905-1930])*, Москва,  1952).  




  [1]: http://en.wikipedia.org/wiki/Naum_Akhiezer
  [2]: http://www.amazon.com/Mathematics-19th-Century-Differential-Variations/dp/0817658459
  [3]: http://www.archive.org/details/sovietmenofscien00turk