High-efficiency kesterite-based thin film solar cells typically feature Cu- poor, Zn-rich absorbers although secondary phases occur easily in non- stoichiometric Cu2ZnSnSe4. We therefore applied high-resolution X-ray fluorescence analysis using a synchrotron nanobeam to study the local composition of a CZTSe cross section lamella cut from a sample with an integral composition of Zn/Sn = 1.37 and Cu/(Zn+Sn) = 0.55. We find submicrometer-sized ZnSe-, SnSe/SnSe2-, and even CuSe/Cu2Se-like secondary phases, while the local compositions of the kesterite are highly Zn-rich yet barely Cu-poor with 1.5 ≤ Zn/Sn ≤ 2.2 and Cu/(Zn+Sn) ∼ 1.0. Consequently, great care must be taken when relating the integral composition to other material properties including the device performance.