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 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 notatin.



-----------------------------------------------------------------------------------------


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


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