In this paper, the author uses Hobby Rice Theorem to produce a simple proof for the fact that the Classical Banach space  admits no finite dimensional Chebyshev subspaces. This fact was mentioned first in Ahiezer and Krein [1]. In article 4 of [1], Krein studied the L-problem in an abstract normed space. From this study, one can indirectly conclude the above mentioned fact. The proof given in [1] is not direct and very difficult to be concluded, the notations and symbols are different, but all the other authors refer to it. The new proof in this paper is direct, clear and simple.

Chebyshev spaces, best approximation, Hobby Rice Theorem,