The electrical mobility of mass-selected single poly(ethylene glycol) (PEG) chains of mass m (< 14 kDalton) and charge state z (+1 to +5) reveals a near-spherical shape above a critical mass m*(z) similar to z(2). The abrupt unfolding observed at m < m*(z) shows that the polymer molecules behave as liquid drops upon reaching the Rayleigh limit, with an apparent surface energy of 0.026 N/m at ion diameters from 1.7 to 3.2 nm. Other nonspherical shape families with structures independent of charge, and with charge-dependent stability domains, are observed. Highly charged ions adopt approximately linear highly stretched configurations where the mobility depends only on m/z, independently of z. An operational definition of the surface energy of a single long chain molecule that is computable and agrees with the measured surface energy is provided.