Mason and Skinner recently constructed a chiral infinite tension limit of the Ramond-Neveu-Schwarz superstring which was shown to compute the Cachazo-He-Yuan formulae for tree-level d=10 Yang-Mills amplitudes and the NS-NS sector of tree-level d=10 supergravity amplitudes. In this letter, their chiral infinite tension limit is generalized to the pure spinor superstring which computes a d=10 superspace version of the Cachazo-He-Yuan formulae for tree-level d=10 super-Yang-Mills and supergravity amplitudes.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)ICTP South American Institute for Fundamental Research, Instituto de F´ısica Te´orica, UNESP — Univ. Estadual Paulista, Rua Dr. Bento T. Ferraz 271, 01140-070, S˜ao Paulo, SP, Brasil.CNPq: 300256/94-9FAPESP: 2009/50639-2FAPESP: 2011/11973-4