The Moon undergoes periodic tidal forcing due to its eccentric and oblique orbit around the Earth¹. The response to this tidal interaction drives temporal changes in the lunar gravity field and is sensitive to the satellite’s internal structure^{2, 3–4}. We use data from the NASA GRAIL spacecraft^{5, 6, 7, 8–9} to recover the time-varying lunar gravity field, including a degree-3 gravitational tidal Love number, k₃. Here, we report our estimated value of k₃ = 0.0163 ± 0.0007, which is about 72% higher than that expected for a spherically symmetric moon¹⁰. Such a large k₃ can be explained if the elastic shear modulus of the mantle varies by about 2–3% between the nearside and farside⁴, providing an observational demonstration of lateral heterogeneities in the deep lunar interior. This asymmetric structure suggests preservation of a predominantly thermal anomaly of roughly 100–200 K in the nearside mantle that formed surface mare regions 3–4 billion years ago¹¹ and could influence the spatial distribution of deep moonquakes¹².