Recently, different measurements of the surface tension γ of liquid helium have given values that differ from each other by as much as 6%. In this paper we report a measurement in which we have studied a helium drop that was magnetically levitated. From measurements of the radius of the drop and the frequencies of the vibrational normal modes, the surface tension could be determined. Measurements were made over the temperature range 0.6 K to 1.6 K, and from an extrapolation, it was estimated that the value of γ at T=0 K is 0.375+/-0.004 dyne cm-1. The trap potential resulted in small shifts of the frequencies of the vibrational modes. We have developed a theory of these shifts and find good agreement with the experimental measurements.