Molecular structure, a key concept of chemistry, has remained elusive from the perspective of all-particle quantum mechanics, despite many efforts. Viewing molecular structure as a manifestation of strong statistical correlation between nuclear positions, we propose a practical method based on Markov chain Monte Carlo sampling and unsupervised machine learning. Application to the D3+ molecule unambiguously shows that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of the molecular structure from fundamental quantum principles.