  We have performed $^{125}$Te NMR on a single crystal of the novel layered
superconductor Fe$_{1.04}$Te$_{0.67}$Se$_{0.33}$ for the first time. The spin
parts of the Knight shifts for both $H // a$, $H // c$ are suppressed in the
superconducting state, indicating the spin singlet superconductivity. At
superconducting state, $1/T_{1}$ shows the power-law behavior ($\sim T^{3}$)
without any coherent peaks. Observations of the residual density of state and
the $T^{3}$-law indicate the presence of the line node in the superconducting
gap. In the normal state, $1/T_{1}T$ which probes the \textbf{q}-summation of
spin fluctuations enhances at low temperatures. Our results suggest that the
superconductivity in Fe$_{1+\delta}$Te$_{1-x}$Se$_{x}$ is stabilized by the
growth of the antiferromagnetic spin fluctuations as well as in FeSe.
