Born in Genoa, Chiesa made his early playing footsteps at amateur club Pontedecimo (1986–87). He then moved to Sampdoria, for which he made his debut on 16 April 1989 in a 1–0 loss at Roma in the 1988–89 Serie A. He then played for Teramo of Serie C2 and successively Chieti of Serie C1 before returning to Sampdoria in 1992. Failing to impress, he then joined Modena in Serie B for the 1993–94 season, and later Cremonese during the 1994–95 season, where he scored 14 goals in their Serie A campaign. In 1995, he returned again with the "blucerchiati", forming a notable attacking duo with Roberto Mancini, and scoring 22 goals in 27 matches in Serie A.