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Spectral observations of the type-IIb supernova (SN) 2016gkg at 300-800 days are reported. The spectra show nebular characteristics, revealing emission from the progenitor star's metal-rich core and providing clues to the kinematics and physical conditions of the explosion. The nebular spectra are dominated by emission lines of [O I] $λ\lambda6300, 6364$ and [Ca II] $λ\lambda7292, 7324$. Other notable, albeit weaker, emission lines include Mg I] $\lambda4571$, [Fe II] $\lambda7155$, O I $\lambda7774$, Ca II triplet, and a broad, boxy feature at the location of H$α$. Unlike in other stripped-envelope SNe, the [O I] doublet is clearly resolved due to the presence of strong narrow components. The doublet shows an unprecedented emission line profile consisting of at least three components for each [O I]$\lambda6300, 6364$ line: a broad component (width $\sim2000$ km s$^{-1}$), and a pair of narrow blue and red components (width $\sim300$ km s$^{-1}$) mirrored against the rest velocity. The narrow component appears also in other lines, and is conspicuous in [O I]. This indicates the presence of multiple distinct kinematic components of material at low and high velocities. The low-velocity components are likely to be produced by a dense, slow-moving emitting region near the center, while the broad components are emitted over a larger volume. These observations suggest an asymmetric explosion, supporting the idea of two-component ejecta that influence the resulting late-time spectra and light curves. SN 2016gkg thus presents striking evidence for significant asymmetry in a standard-energy SN explosion. The presence of material at low velocity, which is not predicted in 1D simulations, emphasizes the importance of multi-dimensional explosion modeling of SNe.