  Spin squeezing can improve atomic precision measurements beyond the standard
quantum limit (SQL), and unitary spin squeezing is essential for improving
atomic clocks. We report substantial and nearly unitary spin squeezing in
$^{171}$Yb, an optical lattice clock atom. The collective nuclear spin of $\sim
10^3$ atoms is squeezed by cavity feedback, using light detuned from the
system's resonances to attain unitarity. The observed precision gain over the
SQL is limited by state readout to 6.5(4) dB, while the generated states offer
a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a
squeezed state within 30% of unitarity, we demonstrate an interferometer that
improves the averaging time over the SQL by a factor of 3.7(2). In the future,
the squeezing can be simply transferred onto the optical clock transition of
$^{171}$Yb.
