  The Neutron Star Interior Composition Explorer (NICER) is an X-ray
astrophysics payload on the International Space Station. It enables
unprecedented high-precision timing of millisecond pulsars without the pulse
broadening and delays due to dispersion and scattering within the interstellar
medium that plague radio timing. We present initial timing results from a year
of data on the millisecond pulsars PSR B1937+21 and PSR J0218+4232, and nine
months of data on PSR B1821-24. NICER time-of-arrival uncertainties for the
three pulsars are consistent with theoretical lower bounds and simulations
based on their pulse shape templates and average source and background photon
count rates. To estimate timing stability, we use the $\sigma_z$ measure, which
is based on the average of the cubic coefficients of polynomial fits to subsets
of timing residuals. So far we are achieving timing stabilities $\sigma_z
\approx 3 \times 10^{-14}$ for PSR B1937+21 and on the order of $10^{-12}$ for
PSRs B1821$-$24 and J0218+4232. Within the span of our \textit{NICER} data we
do not yet see the characteristic break point in the slope of $\sigma_z$;
detection of such a break would indicate that further improvement in the
cumulative root-mean-square (RMS) timing residual is limited by timing noise.
We see this break point in our comparison radio data sets for PSR B1821-24 and
PSR B1937+21 on time scales of $> 2$ years.
