We report a slow-light fiber Bragg grating strain sensor with a resolution limited by the extremely low thermodynamic phase fluctuations of the fiber. This was accomplished by using a short grating (4.5 mm) to enhance the thermal phase noise, an ultra-stable interrogation laser to lower the laser frequency noise, and a slow-light mode with a high group index (∼533) to suppress all other noise sources. We demonstrate that in a similar but longer grating (21 mm), the phase noise is suppressed in inverse proportion to the square root of the length, in accordance with theory, leading to a strain resolution as low as 130 fε/√Hz and a minimum detectable length of ∼3×10-15 m at 1.5 kHz.