  Our understanding of reionization has advanced considerably over the past
decade, with several results now demonstrating that the IGM transitioned from
substantially neutral at $z=7$ to largely reionized at $z=6$. However, little
remains known about the sizes of ionized bubbles at $z\gtrsim7$ as well as the
galaxy overdensities which drive their growth. Fortunately, rest-UV
spectroscopic observations offer a pathway towards characterizing these ionized
bubbles thanks to the resonant nature of Lyman-alpha photons. In a previous
work, we presented Ly$\alpha$ detections from three closely-separated
Lyman-break galaxies at $z\simeq6.8$, suggesting the presence of a large ($R>1$
physical Mpc) ionized bubble in the 1.5 deg$^2$ COSMOS field. Here, we present
new deep Ly$\alpha$ spectra of ten UV-bright ($\mathrm{M}_{\mathrm{UV}}^{} \leq
-20.4$) $z\simeq6.6-6.9$ galaxies in the surrounding area, enabling us to
better characterize this potential ionized bubble. We confidently detect
(S/N$>$7) Ly$\alpha$ emission at $z=6.701-6.882$ in nine of ten observed
galaxies, revealing that the large-scale volume spanned by these sources
(characteristic radius $R = 3.2$ physical Mpc) traces a strong galaxy
overdensity ($N/\langle N\rangle \gtrsim 3$). Our data additionally confirm
that the Ly$\alpha$ emission of UV-bright galaxies in this volume is
significantly enhanced, with 40% (4/10) showing strong Ly$\alpha$ emission
(equivalent width$>$25 $\mathrm{\mathring{A}}$) compared to the 8$-$9% found on
average at $z\sim7$. The median Ly$\alpha$ equivalent width of our observed
galaxies is also $\approx$2$\times$ that typical at $z\sim7$, consistent with
expectations if a very large ($R\sim3$ physical Mpc) ionized bubble is allowing
the Ly$\alpha$ photons to cosmologically redshift far into the damping wing
before encountering HI.
