He was admitted in 1929 to the École normale supérieure in Paris.^[1] In 1938 he obtained his doctorate with a thesis on number theory and algebraic geometry. Subsequently he was a professor in Strasbourg.^[2] From 1954 on, and for 22 years, he was the director of the department of pure mathematics at the University of Grenoble.^[3]

He worked on Diophantine approximation and geometry of numbers, where he used both classical and p-adic analytic methods.^[3] He introduced the Chabauty topology to generalise Mahler's compactness theorem from Euclidean lattices to more general discrete subgroups.^[4]

His 1938 doctoral thesis,^[5] developing ideas of Skolem,^[6] is important in algebraic geometry. According to André Weil:

In his beautiful thesis, Chabauty ..., following ideas of Skolem ..., has shown how the method of p-adic completion, with respect to a more or less arbitrary prime p, can yield deep results about varieties over an algebraic number-field; there, as already in Skolem's work, the problem concerns the intersection of an algebraic variety and of a multiplicative group; by p-adic completion, the latter becomes an algebroid variety defined by linear differential equations.^[7]