With 199Hg atoms confined in an optical lattice trap in the Lamb-Dicke regime, we obtain a spectral line at 265.6 nm for which the FWHM is ~15 Hz. Here we lock an ultrastable laser to this ultranarrow 1S0-3P0 clock transition and achieve a fractional frequency instability of 5.4×10(-15)/✓τ for τ ≤ 400 s. The highly stable laser light used for the atom probing is derived from a 1062.6 nm fiber laser locked to an ultrastable optical cavity that exhibits a mean drift rate of -6.0×10(-17) s(-1) (-16.9 mHz s(-1) at 282 THz) over a six month period. A comparison between two such lasers locked to independent optical cavities shows a flicker noise limited fractional frequency instability of 4×10(-16) per cavity.