The study of distant galaxy groups and clusters at the peak epoch of star formation is limited by the lack of a statistically and homogeneously selected and spectroscopically confirmed sample. Recent discoveries of concentrated starburst activities in cluster cores have opened a new window to hunt for these structures based on their integrated IR luminosities. Here, we carry out a large NOEMA (NOrthern Extended Millimeter Array) program targeting a statistical sample of infrared-luminous sources associated with overdensities of massive galaxies at z > 2, the Noema formIng Cluster survEy (NICE). We present the first result from the ongoing NICE survey, a compact group at z = 3.95 in the Lockman Hole field (LH-SBC3), confirmed via four massive (M⋆ ≳ 1010.5 M⊙) galaxies detected in the CO(4-3) and [CI](1-0) lines. The four CO-detected members of LH-SBC3 are distributed over a 180 kpc physical scale and the entire structure has an estimated halo mass of ∼1013 M⊙ and total star formation rate of ∼4000 M⊙ yr−1. In addition, the most massive galaxy hosts a radio-loud active galactic nucleus with L1.4 GHz, rest = 3.0 × 1025 W Hz−1. The discovery of LH-SBC3 demonstrates the feasibility of our method to efficiently identify high-z compact groups or cluster cores undergoing formation. The existence of these starbursting cluster cores up to z ∼ 4 provides critical insights into the mass assembly history of the central massive galaxies in clusters.