His onstage musical delivery met with positive reviews from the paper El Progresso and the magazine Le Courier des Etats Unis.

In 1904, he submitted a group of his musical compositions for piano and orchestra to the Universal Exposition that was being held that year in St. Louis, Missouri, from 30 April through 1 December, and these were awarded a gold medal.

In 1914, Chavier organized a far-reaching Musical Competition that was sponsored by the Liga Progresista de Ponce and held in that city that same year.

He created compositions for piano with two and four hands versions, for military ensembles, for orchestras and for string instruments.

He also wrote Andante Cantabile Expresivo, the Obertura Puerto Rico for orchestra and Variaciones for the piano.

[13] Among Chavier Arévalo's students was Luis A. Ferré, a concert-level pianist who would later become governor of Puerto Rico.