Born in Treviso, Veneto, Chinellato started his career in various Treviso clubs. Chinellato played for AC Casier–Dosson until 2004. Chinellato was signed by Conegliano in 2004 but released in December 2004. Chinellato was the member of ASD Cipriano–Catron's Allievi B team in Veneto regional Allievi League Second Division in 2006–07 season. The team was located in San Cipriano frazione of Roncade. Chinellato left for Venezia'sAllievi U17 team in 2007–08 season, for Campionato Nazionale Allievi. The team entered the quarter-finals of the playoffs. Chinellato was promoted to the reserve in 2008–09 season, for Campionato Nazionale Dante Berretti, the Lega Pro version of the reserve league.
Chinellato started his professional career at the capital of Veneto region, in Venice. During his Venezia career, he was selected to Italy U20 Serie C team in 2009 Lega Pro Quadrangular Tournament on 20–22 January. He scored once and finished as the runner-up in that youth tournament. Before the tournament, Chinellato made his debut for Venezia on 11 January 2009. On 2 February 2009 Chinellato left for ACF Fiorentina for €100,000. However, he was released on 19 November 2009. Chinellato only played 3 times for la Viola reserve, all in 2008–09 season.
In January 2010 Chinellato was signed by Genoa and scored 8 goals for the reserve in half-season, as team top-scorer. Along with Stephan El Shaarawy and Antonino Ragusa, they were the protagonist for the reserve to win the reserve league title – Campionato Nazionale Primavera. All 3 attackers were left for Italian clubs in lower divisions in 2010–11 season in temporary deals, which Chinellato was signed by the third division club Reggiana along with Matteo D'Alessandro. That season Genoa also signed Gianmarco Zigoni and Mattia Destro, made Chinellato did not had chance in first team and youth team, and left for professional team to gain experience instead. However, Chinellato only made 2 starts for Reggiana in 2010–11 Lega Pro Prima Divisione. Despite not a regular player in professional matches, Chinellato received his only U20 call-up in February 2011 against Germany. He substituted Andrea Bertolacci in the first half and was substituted by Mattia Montini in the second half.
Milan
In July 2011, Chinellato followed the footsteps of El Shaarawy who joined Milan in June for €10 million. Likes El Shaarawy and Merkel, Chinellato also left for Milan in co-ownership deal for €1.75 million with Nicola Pasini moved to Genoa. That season Milan and Genoa formed four swap deals in total,, which Pelé moved to Milan for €950,000 and Mario Sampirisi to Genoa for €1 million on 30 August 2011. Chinellato–Pasini–Pelé–Sampirisi deals made Milan paid Genoa just €50,000 in net. Chinellato was immediately left for another third division club Südtirol. However, despite Chinellato made more starts, Chinellato scored 3 goals only in 2011–12 Lega Pro Prima Divisione. On 1 June 2012, Genoa bought Pasini and Sampirisi outright; Chinellato and Pelé also moved to Milan outright. All 4 deals for the original price except €50,000 discount for Pelé to make the 4 deals effectively a pure player swap. On 19 July 2012, Chinellato joined Prima Divisione side Tritium on a loan deal. On 27 July 2013, Chinellato signed for Seconda Divisione club Sorrento on another loan deal. On 21 January 2014 he was signed by Cosenza. On 17 July 2014 he was re-signed by Südtirol in a 2-year loan. On 31 August 2015 Chinellato was signed by Cuneo in a temporary deal.
Como
On 18 July 2016 Chinellato was signed by Calcio Como.
Padova
On 16 January 2019, he joined Gubbio on loan until the end of the 2018–19 season.
