  We have performed a comprehensive spectral and timing analysis of the first
NuSTAR observation of the high-mass X-ray binary 4U 1538-522. The observation
covers the X-ray eclipse of the source, plus the eclipse ingress and egress. We
use the new measurement of the mid-eclipse time to update the orbital
parameters of the system and find marginally-significant evolution in the
orbital period, with $\dot{P}_{\rm orb}/P_{\rm orb} = \left(-0.95 \pm
0.37\right) \times 10^{-6}$ yr$^{-1}$. The cyclotron line energy is found
approximately 1.2 keV higher than RXTE measurements from 1997--2003, in line
with the increased energy observed by Suzaku in 2012 and strengthening the case
for secular evolution of 4U 1538-522's CRSF. We additionally characterize the
behavior of the iron fluorescence and emission lines and line-of-sight
absorption as the source moves into and out of eclipse.
