  In dense stellar environments, the merger products of binary black hole
mergers may undergo additional mergers. These hierarchical mergers are
predicted to have higher masses than the first generation of black holes made
from stars. The components of hierarchical mergers are expected to have
significant characteristic spins $\chi\sim 0.7$. However, since the population
properties of first-generation black holes are uncertain, it is difficult to
know if any given merger is first-generation or hierarchical. We use
observations of gravitational waves to reconstruct the binary black hole mass
and spin spectrum of a population containing hierarchical merger events. We
employ a phenomenological model that captures the properties of merging binary
black holes from simulations of dense stellar environments. Inspired by recent
work on the isolated formation of low-spin black holes, we include a zero-spin
subpopulation. We analyze binary black holes from LIGO and Virgo's first two
observing runs, and find that this catalog is consistent with having no
hierarchical mergers. We find that the most massive system in this catalog,
GW170729, is mostly likely a first-generation merger, having a $4\%$
probability of being a hierarchical merger assuming a $5 \times 10^5 M_{\odot}$
globular cluster mass. Using our model, we find that $99\%$ of first-generation
black holes in coalescing binaries have masses below 44 $M_{\odot}$, and the
fraction of binaries with near-zero spin is $0.051^{+0.156}_{-0.048}$ ($90\%$
credible interval). Upcoming observations will determine if hierarchical
mergers are a common source of gravitational waves.
