  The Neutron Star Interior Composition Explorer (NICER) has observed seven
thermonuclear X-ray bursts from the Low Mass X-ray Binary (LMXB) neutron star
4U 1728-34 from the start of the mission's operations until February of 2019.
Three of these bursts show oscillations in their decaying tail with frequencies
that are within 1 Hz of the previously detected burst oscillations from this
source. Two of these burst oscillations have unusual properties: They have
large fractional rms amplitudes of $ 48 \pm 9 \%$ and $ 46 \pm 9 \%$, and they
are detected only at photon energies above 6 keV. By contrast, the third
detected burst oscillation is compatible with previous observations of this
source, with a fractional rms amplitude of $7.7 \pm 1.5\%$ rms in the 0.3 to
6.2 keV energy band. We discuss the implications of these large-amplitude burst
oscillations, finding they are difficult to explain with the current
theoretical models for X-ray burst tail oscillations.
