There are a growing number of multi-planet systems known to be orbiting their host stars with orbital periods that place them in mean motion resonances (MMRs). These systems are generally in first-order resonances and dynamical studies have focused their efforts on understanding the origin and evolution of such dynamically resonant commensurabilities. Here we report the discovery of two super-Earths that are close to a second-order dynamical resonance orbiting the metal-poor ([Fe/H] = –0.43 dex) and inactive G2V star HD 41428. We analyzed 62 HARPS archival radial velocities for this star that, until now, exhibited no evidence for planetary companions. Using our new Bayesian Doppler signal detection algorithm, we find two significant signals in the data, with periods of 18.357 days and 25.648 days, indicating they could be part of a 7:5 second-order MMR. Both semi-amplitudes are below 3 m s–1 and the minimum masses of the pair are 12.3 and 8.6 M ⊕, respectively. Our simulations found that apsidal alignment stabilizes the system, and even though libration of the resonant angles was not seen, the system is affected by the presence of the resonance and could still occupy the 7:5 commensurability, which would be the first planetary configuration in such a dynamical resonance. Given the multitude of low-mass multi-planet systems that will be discovered in the coming years, we expect that more of these second-order resonant configurations will emerge from the data, highlighting the need for a better understanding of the dynamical interactions between forming planetesimals.