We prove an upper bound for the number Neg (H) of negative eigenvalues of the Schr¨odinger operator H = −Δ − V in R2, in terms of a weighted Lp-norm of the potential V, for any 1 < p < ∞. This estimate scales correctly (linearly) in α under the transformation V 7→ αV of the potential. In Rn, n ≥ 3, an upper estimate of Neg (H) with a correct scaling in α has been known since 1970s and is due to Cwickel- Lieb-Rosenblum.