Chiricheș began his career at LPS Bacău as a midfielder, even as a striker a few years later when he moved to Ardealul Cluj playing alongside Mihai Răduț and Alexandru Maxim. He then moved to Portuguese side Benfica in 2007.
Upon his return to Romania after 12 months spent in Portugal, Chiricheș joined lower league club Internațional Curtea de Argeș and helped them earn promotion to the top flight Liga I in 2009. In 2010, shortly after Internațional was dissolved, he moved alongside many of his teammates to Pandurii Târgu Jiu. Chiricheș was close to signing with Steaua București instead of Pandurii, but Victor Pițurcă, Steaua's coach at the time, did not agree with the transfer.
Steaua București
After one season, Chiricheș sealed another transfer, this time to FC Steaua București for a reported sum of €700,000 and 25% left to Pandurii in case of a future transfer. Steaua paid €500,000 for the remaining procents of the co-ownership in August 2013, making the total transfer sum to €1.2 million. On 25 October 2012, he scored an overhead volley from near the penalty spot in a 2–0 win against Molde in the Europa League, which put Steaua in control of Group E. Chiricheș scored from long range against Ajax on 21 February 2013, canceling out a two-goal first-leg deficit as Steaua triumphed in the penalty shoot-out to set up a Round of 16 meeting with 2012 Champions League winners, Chelsea. He scored again, an equalising goal to make it 1–1 with a fine close-range finish on the stroke of half-time in the 3–1 second leg loss against "the Blues" at Stamford Bridge after Steaua won the first leg 1–0.
Tottenham Hotspur
On 30 August 2013, English club Tottenham Hotspur paid a then-Romania record sale fee of €9.5 million for the signing of Chiricheș. He made his debut for Tottenham in a 4–0 League Cup victory over Aston Villa on 24 September. His Premier League debut was also an away game against Aston Villa, a 2–0 win on 20 October in which he was voted Man of the Match by fans. On 4 December, Chiricheș scored his first goal for the team, an equaliser from outside the penalty box in a 2–1 victory against Fulham. At the end of the January 2015 transfer window A.S. Roma offered €500,000 to take Chiricheș on a six-month loan, which was deemed too low by Spurs and rejected. On 9 May, he was sent off for two bookings as Tottenham lost 3–0 to Stoke City at the Britannia Stadium.
Napoli
On 30 July 2015, Italian team Napoli signed Chiricheș on a four-year deal for £4.5 million. He made his Serie A debut for Napoli in a 1–2 home loss to Sassuolo. On 10 September 2018, it was announced that Chiricheș had suffered anterior cruciate ligament damage requiring surgery and sidelining him for most of the season.
Sassuolo
On 2 September 2019, Chiricheş joined Serie A club Sassuolo on loan with an obligation to buy for €12 million plus bonuses at the end of the season.
International career
Chiriches made his debut for the senior team in an UEFA Euro 2012 qualifying match against Luxembourg on 2 September 2011. On 14 August 2013, Chiricheș became the captain of Romania, in the friendly draw 1–1 over Slovakia. His competitive debut as captain was on 6 September, a 3–0 victory against Hungary, in a 2014 FIFA World Cup qualifying game. He played his 50th match for the national team on 5 October 2017, against Kazakhstan, in a 3–1 home win, match in which he captained Romania.
