  Cosmological first-order phase transitions (1stOPTs) are said to be strongly
supercooled when the nucleation temperature is much smaller than the critical
temperature. These are often encountered in theories that admit a nearly
scale-invariant potential, for which the bounce action decreases only
logarithmically with temperature. During supercooled 1stOPTs the equation of
state of the universe undergoes a rapid and drastic change, transitioning from
vacuum-domination to radiation-domination. The statistical variations in bubble
nucleation histories imply that distinct causal patches percolate at slightly
different times. Patches which percolate the latest undergo the longest
vacuum-domination stage and as a consequence develop large over-densities
triggering their collapse into primordial black holes (PBHs). We derive an
analytical approximation for the probability of a patch to collapse into a PBH
as a function of the 1stOPT duration, $\beta^{-1}$, and deduce the expected PBH
abundance. We find that 1stOPTs which take more than $12\%$ of a Hubble time to
complete ($\beta/H \lesssim 8$) produce observable PBHs. Their abundance is
independent of the duration of the supercooling phase, in agreement with the de
Sitter no hair conjecture.
