  We present the first photometric analysis of the supernova (SN) impostor AT
2016blu in NGC 4559. This transient was discovered by the Lick Observatory
Supernova Search in 2012 and has continued its outbursts since then. Optical
and infrared photometry of AT 2016blu reveals at least 19 outbursts in
2012-2022. Similar photometry from 1999-2009 shows no outbursts, indicating
that the star was relatively stable in the decade before discovery. Archival
{\it Hubble Space Telescope} observations suggest that the progenitor had a
minimum initial mass of $M >= 33$ M$_{\odot}$ and a luminosity of $L >=
10^{5.7}$ L$_{\odot}$. AT 2016blu's outbursts show irregular variability with
multiple closely spaced peaks having typical amplitudes of 1-2 mag and
durations of 1-4 weeks. While individual outbursts have irregular light curves,
concentrations of these peaks recur with a period of $\sim 113 \pm 2$ d. Based
on this period, we predict times for upcoming outbursts in 2023 and 2024. AT
2016blu shares similarities with SN 2000ch in NGC 3432, where outbursts may
arise from periastron encounters in an eccentric binary containing a luminous
blue variable (LBV). We propose that AT 2016blu's outbursts are also driven by
interactions that intensify around periastron in an eccentric system. Intrinsic
variability of the LBV-like primary star may cause different intensity and
duration of binary interaction at each periastron passage. AT 2016blu also
resembles the periastron encounters of $\eta$ Carinae prior to its Great
Eruption and the erratic pre-SN eruptions of SN 2009ip. This similarity and the
onset of eruptions in the past decade hint that AT 2016blu may also be headed
for a catastrophe, making it a target of great interest.
