The expected universal dynamics associated with the initial stage of droplet coalescence are difficult to study visually due to the rapid motion of the liquid and the awkward viewing geometry. Here we employ an electrical method to study the coalescence of two low-viscosity droplets at early times. We measure the growth dynamics of the bridge connecting the two droplets and observe a new asymptotic regime inconsistent with previous theoretical predictions. The measurements are consistent with a model in which the two liquids coalesce with a slightly deformed interface.