Using a laser that is frequency-locked to a FabryPérotétalon of high finesse and stability, we probe the 5d 10 6s 2 S 1/2 (F=0)↔5d 9 6s 2 2 D 5/2 (F=2) ∆mF =0 electricquadrupole transition of a single laser-cooled 199 Hg + ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm (1.06 × 10 15 Hz), yielding a line Q ≈ 1.6 × 10 14 . We perform a preliminary measurement of the 5d 9 6s 2 2 D 5/2 electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards. PACS numbers: 06.30. Ft, 32.30.Jc, 32.80.Pj, 42.62.Fi Precision spectroscopy has held an enduring place in physics, particularly in the elucidation of atomic structure and the measurement of fundamental constants, in the development of accurate clocks, and for fundamental tests of physical laws. Two ingredients of paramount importance are high accuracy, that is, the uncertainty in systematic frequency shifts must be small, and high signal-to-noise ratio, since the desired measurement precision must be reached in a practical length of time. In this paper, we report the measurement of an optical absorption line in a single laser-cooled 199 Hg + ion at a frequency ν 0 = 1.06 × 10 15 Hz (wavelength ≈ 282 nm) for which a linewidth ∆ν = 6.7 Hz is observed, yielding the highest Q ≡ ν 0 /∆ν ever achieved for optical (or lower frequency) spectroscopy. We also report a preliminary measurement of the interaction of the upper state electric-quadrupole moment with the static field gradients of the ion trap, which is expected to contribute the largest uncertainty for a frequency standard based on this system.In spectroscopy and for clocks, fluctuations in frequency measurement are usually expressed fractionally: σ y (τ ) = ∆ν meas (τ )/ν 0 , where τ is the total measurement time. When the stability is limited by quantum fluctuations in state detection,2 , where N is the number of atoms, τ probe is the transition probe time (typically limited by the excited-state lifetime or the stability of the local oscillator), and C is a constant of order unity that depends on the method of interrogation. For many decades, the highest accuracies and the greatest stabilities have been achieved by locking a microwave oscillator to a hyperfine transition in an atomic ground state [1][2][3][4][5]. Since the fractional instability σ y (τ ) is inversely proportional to the transition frequency, greater stability can be attained using transitions at higher frequencies such as those in the optical region of the electromagnetic spec-