  We report on the results of the first search for the production of axion-like
particles (ALP) via Primakoff production on nuclear targets using the GlueX
detector. This search uses an integrated luminosity of 100
pb$^{-1}\cdot$nucleon on a $^{12}$C target, and explores the mass region of 200
< $m_a$ < 450 MeV via the decay $X\rightarrow\gamma\gamma$. This mass range is
between the $\pi^0$ and $\eta$ masses, which enables the use of the measured
$\eta$ production rate to obtain absolute bounds on the ALP production with
reduced sensitivity to experimental luminosity and detection efficiency. We
find no evidence for an ALP, consistent with previous searches in the quoted
mass range, and present limits on the coupling on the scale of $O$(1 TeV). We
further find that the ALP production limit we obtain is hindered by the peaking
structure of the non-target-related dominant background in GlueX, which we
treat by using data on $^4$He to estimate and subtract these backgrounds. We
comment on how this search can be improved in a future higher-statistics
dedicated measurement.
