Most of the presently identified exoplanets have masses similar to that of Jupiter and therefore are assumed to be gaseous objects. With the ever-increasing interest in discovering lower mass planets, several of the so-called super-Earths (1M_⊕ <M < 10M_⊕), which are predicted to be rocky, have already been found. Here we report the possible discovery of a planet around the M-type star GJ 436 with a minimum mass of 4.7 ± 0.6M_⊕ and a true mass of ~5M_⊕, which would make it the least massive planet around a main-sequence star found to date. The planet is identified from its perturbations on an inner Neptune-mass transiting planet (GJ 436b), by pumping eccentricity and producing variations in the orbital inclination. Analysis of published radial velocity measurements indeed reveals a significant signal corresponding to an orbital period that is very close to the 2:1 mean motion resonance with the inner planet. The near-grazing nature of the transit makes it extremely sensitive to small changes in the inclination.