  We report Keck-NIRSPEC observations of the Brackett $\alpha$ 4.05 $\mu$m
recombination line across the two candidate embedded super star clusters (SSCs)
in NGC 1569. These SSCs power a bright HII region and have been previously
detected as radio and mid-infrared sources. Supplemented with high resolution
VLA mapping of the radio continuum along with IRTF-TEXES spectroscopy of the
[SIV] 10.5 $\mu$m line, the Brackett $\alpha$ spectra data provide new insight
into the dynamical state of gas ionized by these forming massive clusters. NIR
sources detected in 2 $\mu$m images from the Slit-viewing Camera are matched
with GAIA sources to obtain accurate celestial coordinates and slit positions
to within $\sim 0.1''$. Br$\alpha$ is detected as a strong emission peak
powered by the less luminous infrared source, MIR1 ($L_{\rm IR}\sim
2\times10^7~L_\odot$). The second candidate SSC MIR2 is more luminous ($L_{\rm
IR}\gtrsim 4\times10^8~L_\odot$) but exhibits weak radio continuum and
Br$\alpha$ emission, suggesting the ionized gas is extremely dense ($n_e\gtrsim
10^5$ cm$^{-3}$), corresponding to hypercompact HII regions around newborn
massive stars. The Br$\alpha$ and [SIV] lines across the region are both
remarkably symmetric and extremely narrow, with observed line widths $\Delta v
\simeq 40$ km s$^{-1}$, FWHM. This result is the first clear evidence that
feedback from NGC 1569's youngest giant clusters is currently incapable of
rapid gas dispersal, consistent with the emerging theoretical paradigm in the
formation of giant star clusters.
