We study the high-energy asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface $M$ of Anosov type. To do this, we look at families of distributions associated to them on the cotangent bundle $T^*M$ and we derive entropic properties on their accumulation points in the high-energy limit (the so-called semiclassical measures). We show that the Kolmogorov-Sinai entropy of a semiclassical measure $\mu$ for the geodesic flow $g^t$ is bounded from below by half of the Ruelle upper bound; that is, \[h_{KS}(\mu,g)\geq \frac{1}{2}\int_{S^*M} \chi^+(\rho)\ d\!\mu(\rho),\] where $\chi^+(\rho)$ is the upper Lyapunov exponent at point $\rho$ .