Surface grating couplers are diffractive periodic structures that enable efficient coupling of light between optical fibers and planar waveguides. Conventional grating couplers have polarization specific and limited wavelength operation, because of the intrinsic radiation angle dependency on both wavelength and polarization. In this Letter, we propose, to the best of our knowledge, the first polarization-independent surface fiber-chip grating coupler, behaving as a wavelength splitter for the O and C communication bands. Polarization insensitivity is achieved by subwavelength segmentation of the silicon gratings, together with a novel design to allow the dual wavelengths to propagate along two opposite directions in the chip. For the TE and TM polarizations, coupling efficiencies around -4.5 dB are achieved at both 1310 nm and 1550 nm, with an average 1-dB bandwidth of ~45 nm and ~60 nm, respectively. This grating coupler concept can be used as a part of transceivers to increase the data rate of wavelength-division-multiplexing (WDM) systems for fiber-to-the-home (FTTH) network services.