We report a numerical and experimental study of an on-chip optical spectrometer, utilizing propagating surface plasmon polaritons in the telecom spectral range. The device is based on two holographic gratings, one for coupling, and the other for decoupling free-space radiation with the surface plasmons. This 800 μm×100 μm on-chip spectrometer resolves 17 channels spectrally separated by 3.1 nm, spanning a freely tunable spectral window, and is based on standard lithography fabrication technology. We propose two potential applications for this new device; the first employs the holographic control over the amplitude and phase of the input spectrum, for intrinsically filtering unwanted frequencies, like pump radiation in Raman spectroscopy. The second prospect utilizes the unique plasmonic field enhancement at the metal-dielectric boundary for the spectral analysis of very small samples (e.g., Mie scatterers) placed between the two gratings.