The south west London side kicked off their Premier League campaign with a comfortable 3-0 home win against Crystal Palace on Saturday, with Marcos Alonso, Christian Pulisic and Trevoh Chalobah scoring their goals against the Eagles.
Chelsea FC have spent big on bolstering their attacking options this summer, with the Blues having brought in striker Romelu Lukaku from Inter Milan in a big-money deal.
Thomas Tuchel will be aiming for his side to be one of the main contenders for the Premier League title this season after they finished in fourth place in the table last term.
And former Manchester United and England star Neville is certain that Chelsea FC will be amongst the main challengers for the top-flight crown this season.
Speaking to Sky Sports on Sunday, Neville said: “They [Chelsea FC] are going to be serious this season."