We analyze the implications of the new physics effect seen in the g -- 2 Brookhaven measurement and show that if the effect arises from supersymmetry, then the sign of the Higgs mixing parameter mu is determined to be positive in the standard sign convention. Further, analyses within the minimal supergravity model show that the Brookhaven result leads to upper limits on the universal gaugino and scalar masses of m(1/2) < or = 800 GeV and m(0) < or = 1.5 TeV for tan beta < or = 55. Our analysis strongly suggests that supersymmetry via production of sparticles must be found at the CERN Large Hadron Collider. Further, sgn(mu) positive is favorable for the discovery of supersymmetric cold dark matter.