We develop a method to infer or rule out the presence of an atmosphere on a tidally locked hot super Earth. The question of atmosphere retention is a fundamental one, especially for planets orbiting M stars due to the star's long-duration active phase and corresponding potential for stellar-induced planetary atmospheric escape and erosion. Tidally locked planets with no atmosphere are expected to show a Lambertian-like thermal phase curve, causing the combined light of the planet-star system to vary with planet orbital phase. We report Spitzer 8 μm IRAC observations of GJ 876 taken over 32 continuous hours and reaching a relative photometric precision of 3.9 × 10^–4 per point for 25.6 s time sampling. This translates to a 3σ limit of 5.13 × 10^–5 on a planet thermal phase curve amplitude. Despite the almost photon-noise-limited data, we are unable to conclusively infer the presence of an atmosphere or rule one out on the non-transiting short-period super Earth GJ 876d. The limiting factor in our observations was the miniscule, monotonic photometric variation of the slightly active host M star, because the partial sine wave due to the planet has a component in common with the stellar linear trend. The proposed method is nevertheless very promising for transiting hot super Earths with the James Webb Space Telescope and is critical for establishing observational constraints for atmospheric escape.