We show that electric field noise from surface charge fluctuations can be a significant source of spin decoherence for near-surface nitrogen-vacancy (NV) centers in diamond. This conclusion is based on the increase in spin coherence observed when the diamond surface is covered with high-dielectric-constant liquids, such as glycerol. Double resonance experiments show that improved coherence occurs even though the coupling to nearby electron spins is unchanged when the liquid is applied. Multipulse spin echo experiments reveal the effect of glycerol on the spectrum of NV frequency noise.