  We examine the cooling radiation from forming galaxies in hydrodynamic
simulations of the LCDM model (cold dark matter with a cosmological constant),
focusing on the Ly-alpha line luminosities of high-redshift systems. Primordial
composition gas condenses within dark matter potential wells, forming objects
with masses and sizes comparable to the luminous regions of observed galaxies.
As expected, the energy radiated in this process is comparable to the
gravitational binding energy of the baryons, and the total cooling luminosity
of the galaxy population peaks at z ~= 2. However, in contrast to the classical
picture of gas cooling from the \sim 10^6 K virial temperature of a typical
dark matter halo, we find that most of the cooling radiation is emitted by gas
with T < 20,000 K. As a consequence, roughly 50% of this cooling radiation
emerges in the Ly-alpha line. While a galaxy's cooling luminosity is usually
smaller than the ionizing continuum luminosity of its young stars, the two are
comparable in the most massive systems, and the cooling radiation is produced
at larger radii, where the Ly-alpha photons are less likely to be extinguished
by dust. We suggest, in particular, that cooling radiation could explain the
two large (\sim 100 kpc), luminous (L_{Ly-alpha} \sim 10^{44} erg s^{-1})
``blobs'' of Ly-alpha emission found in Steidel et al.'s (1999) narrow band
survey of a z = 3 proto-cluster. Our simulations predict objects of the
observed luminosity at about the right space density, and radiative transfer
effects can account for the observed sizes and line widths. We discuss
observable tests of this hypothesis for the nature of the Ly-alpha blobs, and
we present predictions for the contribution of cooling radiation to the
Ly-alpha luminosity function of galaxies as a function of redshift.
