Given a bi-invariant metric on a compact Lie group G, it is well known that the sectional curvature of 2 orthonormal left invariant vector fields U and V can be expressed as K(U,V) = 1/4||[U,V]||^2. In particular, G has non-negative sectional curvature. In direct contrast, we will prove the following theorem (due to Wallach), without using the classification of semi-simple lie algebras: Let G be any compact Lie group with left invariant metric. Assume G has positive curvature. Then G is diffeomorphic to S^3 or SO(3).