Let U be a finite dimensional subspace of \(C_ 1(K)\), the continuous functions normed with the \(L_ 1\) norm. K is a compact subset of \(R^ n\) and equal the closure of its inerior. This paper proves that there is a continuous selection for the metric projection onto U only in the trivial case that U is a Chebyshev set. This tidy theorem for such a basic setting well supplements the few similar results in the literature for other spaces. In fact it is shown that if K is connected there does not exist a selection, s, for the metric projection such that even \(f_ n\) converging uniformly to f does not mandate the convergence of \(s(f_ n)\) to s(f). The proofs involve a series of lemmas manipulating the characterization of best approximations in \(C_ 1(K)\) and the substructures forced upon U by the existence of a continuous selection for the metric projection.