To solve \(-127 + \frac{3}{14}\), we first convert \(-127\) into a fraction.
We can express \(-127\) as \(-\frac{127 \times 14}{14}\) to have a common denominator. This gives us:
\[ -127 = -\frac{1778}{14} \]
Now, we can add the two fractions:
\[ -\frac{1778}{14} + \frac{3}{14} = \frac{-1778 + 3}{14} = \frac{-1775}{14} \]
Thus, the answer is:
\[ \boxed{\frac{-1775}{14}} \]