Chuks Aneke joined Arsenal in 2001, age seven, and progressed through the academy. He made his reserves debut against Maidenhead United in a pre-season friendly on 28 July 2009. Aneke, along with fellow academy player Benik Afobe, were offered the chance to visit FC Barcelona's training base with view to signing for them. However, he instead signed a professional contract with Arsenal in July 2010.
Ahead of the 2011–12 season, Aneke signed a contract extension with the club. He scored for Arsenal's reserve side in friendly victories against Woking, Hastings United, and Stevenage respectively. He finally made his competitive first team debut for Arsenal in the club's 3–1 League Cup victory against Shrewsbury Town on 20 September 2011, coming on as a 90th-minute substitute in the match.
Aneke joined League One side Stevenage on 22 November 2011, on a loan deal until January 2012. He made his debut for the club on 26 November, in Stevenage's 0–0 home draw with Walsall. Aneke was sent-off for a high-footed challenge in a 1–0 defeat to Leyton Orient on 2 January 2012, resulting in a three-game suspension It was later announced that Aneke would remain on loan at Stevenage until March 2012, with a view to extending the loan until the end of the 2011–12 season.
Aneke returned to his parent club on 5 March, and, on the same day, scored in a 2–0 reserve victory against Chelsea reserves. Linking-up with his manager at Stevenage, Graham Westley, on 22 March 2012 Aneke joined League One team Preston North End on-loan until the end of the 2011–12 season. On 24 March he made a scoring debut in a 1–1 draw against Bury.
In September 2012, Aneke joined Crewe Alexandra on a month's loan, making his debut as a second-half substitute against Tranmere Rovers on 8 September. He started the following fixture, away at Stevenage, but received a second-half red card for a two-footed tackle, serving a three-match suspension. Aneke's loan spell with the club was extended until January, and later extended further until the end of the season. On 2 August 2013, Aneke returned to Crewe on a six-month loan from Arsenal, which was again later extended until the end of the season.
After thirteen seasons, Aneke left Arsenal in June 2014 at the expiry of his contract.
On 21 June 2014, Zulte Waregem announced the signing of Aneke on a three-year contract following his release by Arsenal. Over the following two seasons which were interrupted by injury, Aneke made a total of 41 appearances in all competitions, scoring four goals.
On 2 August 2016, whilst still recovering from an injury sustained at his previous club Zulte Waragem, Aneke joined League One side Milton Keynes Dons, signing a one-year deal with an option of a second year. On 22 November 2016, following almost twelve months on the sidelines through injury, Aneke made his league debut for the club, coming on as an 84th-minute substitute in a 2–3 home defeat to Chesterfield. He scored his first goals for the club, scoring twice in a 5–3 home win over Northampton Town on 21 January 2017. On 28 January 2017 Aneke scored two goals against Peterborough United. On 17 August 2017, Aneke signed an extended contract keeping him at the club until June 2019.
After scoring 19 goals for MK Dons, Chuks signed for SkyBet Championship side Charlton Athletic on June 28th 2019.