We formulate a refinement of $SU(N)$ Chern-Simons theory via the refined topological string. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle action. We give an explicit solution of the theory, in terms of a one-parameter refinement of the $S$ and $T$ matrices of Chern-Simons theory, related to the theory of Macdonald polynomials. The ordinary and refined Chern-Simons theory are similar in many ways; for example, the Verlinde formula holds in both. We obtain new topological invariants of Seifert three-manifolds and torus knots inside them. We conjecture that the knot invariants we compute are the Poincare polynomials of the $sl(n)$ knot homology theory. The latter includes the Khovanov-Rozansky knot homology, as a special case. The conjecture passes a number of nontrivial checks. We show that, for a large number of torus knots colored with the fundamental representation of $SU(N)$, our knot invariants agree with the Poincare polynomials of Khovanov-Rozansky homology. As a byproduct, we show that our theory on $S^3$ has a dual description in term of the refined topological string on $X=\mathcal{O}(-1)\oplus \mathcal{O}(-1) \to \mathbb{P}^1$. This supports the conjecture by Gukov, Schwarz and Vafa relating the spectrum of BPS states on $X$ to $sl(n)$ knot homology.