This paper gives the first algorithm for finding a set of natural ε-clusters of complex zeros of a triangular system of polynomials within a given polybox in C^n, for any given ε > 0. Our algorithm is based on a recent near-optimal algorithm of Becker et al (2016) for clustering the complex roots of a univariate polynomial where the coefficients are represented by number oracles. Our algorithm is numeric, produces guaranteed results and is based on subdivision. We implemented it and compared it with state of the art solvers on various triangular systems, including systems with clusters of solutions or multiple solutions.