  We have measured the spin susceptibility of the underdoped high temperature
superconductor, YBa2Cu4O8 by Gd^{3+} electron spin resonance in single crystals
and aligned powders at several magnetic fields between 3 and 15.4 T. At low
temperatures and high fields, the spin susceptibility of the CuO2 planes is
enhanced slightly in the $B\parallel c$ orientation with respect to the $B\perp
c$ orientation. The enhancement in an applied field of 15.4 T ($\approx 0.15
H_{c2}$) at 16 K (0.2 $T_c$) is approximately 10 percent of the susceptibility
measured at $T_c$. Such a small magnitude suggests that the second critical
field of superconductivity, $H_{c2}\approx 100 T$, would not suppress the
pseudogap. This work demonstrates the potential of high field ESR in single
crystals for studying high $T_c$ superconductors.
