The first measurement of energy produced transverse to the beam direction at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory is presented. The midrapidity transverse energy density per participating nucleon rises steadily with the number of participants, closely paralleling the rise in charged-particle density, such that <E(T)>/<N(ch)> remains relatively constant as a function of centrality. The energy density calculated via Bjorken's prescription for the 2% most central Au+Au collisions at square root[s(NN)] = 130 GeV is at least epsilon(Bj) = 4.6 GeV/fm(3), which is a factor of 1.6 larger than found at sqrt[s(NN)] = 17.2 GeV ( Pb+Pb at CERN).