  We report the detection of 158 micron [CII] fine-structure line emission from
MIPS J142824.0+352619, a hyperluminous (L_IR ~ 10^13 L_sun) starburst galaxy at
z=1.3. The line is bright, and corresponds to a fraction L_[CII]/L_FIR = 2 x
10^-3 of the far-IR (FIR) continuum. The [CII], CO, and FIR continuum emission
may be modeled as arising from photodissociation regions (PDRs) that have a
characteristic gas density of n ~ 10^4.2 cm^-3, and that are illuminated by a
far-UV radiation field ~10^3.2 times more intense than the local interstellar
radiation field. The mass in these PDRs accounts for approximately half of the
molecular gas mass in this galaxy. The L_[CII]/L_FIR ratio is higher than
observed in local ULIRGs or in the few high-redshift QSOs detected in [CII],
but the L_[CII]/L_FIR and L_CO/L_FIR ratios are similar to the values seen in
nearby starburst galaxies. This suggests that MIPS J142824.0+352619 is a
scaled-up version of a starburst nucleus, with the burst extended over several
kiloparsecs.
