The champions visit Livorno on Sunday looking to extend their four-match winning streak.
Juve's 3-0 triumph against Napoli in Turin last time out saw Antonio Conte's side climb into second place and reduce the gap with league leaders Roma to just one point.
The win was Juve's 10th in 12 league games and kept the Turin giants perfect at home.
"We are on the right path," Chiellini said. "But we know that it takes very little for things to change and that is why we must continue to work hard, focus on ourselves and not on others.
"We now have three games against teams - Livorno, Udinese and Bologna - that are in need of points and that will no doubt give 110 per cent against us.
"All will depend on the approach we have."
Livorno have won just one of their last nine league games and their 2-0 defeat at Inter Milan in the last round dropped them to 15th place, three points clear of the relegation zone.
The Amaranto will be hoping Juve will be distracted by their Champions League match against FC Copenhagen on Wednesday.
The Bianconeri need to beat the Danes in Turin if they are to have any chance of progressing to the knockout round of the competition.
"We know we face a huge task against the defending champions," Livorno coach Davide Nicola said. "We have to show courage and determination to try and stop Juve from taking three points.
"We showed positive signs against Inter but we still have a lot of room for improvement."
Fortunately for Livorno, Juve will be nowhere near full strength with regular defenders Stephan Lichtsteiner and Andrea Barzagli out injured and Leonardo Bonucci and Angelo Ogbonna suspended.
The hosts will be bolstered by the return of defenders Andrea Coda and Leandro Rinaudo as well as midfielder Leandro Greco from suspension.
However, Livorno's top scorer Paulinho must serve a one-match ban.