Confronted with considerable intermittence and variability of wind power, prediction intervals (PIs) serve as a crucial tool to assist power system decision-making under uncertainties. Conventional PIs rely on predetermining the lower and upper quantile proportions and therefore suffer from conservative interval width. This paper innovatively develops a chance constrained extreme learning machine (CCELM) model to generate quality nonparametric proportion-free PIs of wind power generation, which minimizes the expected interval width subject to the PI coverage probability constraint. Due to the independency on the preset PI bounds proportions, the proposed CCELM model merits high adaptivity and taps the latent potentialities for PI shortening. The convexity of extreme learning machine renders the sample average approximation counterpart of stochastic CCELM model equivalent to a parameter searching task in parametric optimization problem with polyhedral feasible region. A novel difference of convex functions optimization based bisection search (DCBS) algorithm is proposed to efficiently construct the CCELM model, which successfully realizes machine learning by means of solving linear programming problems sequentially. Comprehensive numerical experiments based on actual wind farm data demonstrate the significant effectiveness and efficiency of the developed CCELM model and DCBS algorithm.