Mamelodi Sundowns are at home to Lamontville Golden Arrows, while defending champions SuperSport United travel to another giant-killing side, KwaDukuza United.
Acornbush defeated Cape Town City in the Last 32 and will be relishing hosting Chiefs at the Kwabokeni Stadium just outside of Nelspruit.
They will be hoping to repeat the feat of then-third-tier outfit Baroka FC when they beat AmaKhosi in the quarterfinals in 2011.
Pirates beat Stars 4-2 in the semifinals last season but it is a tough away day for the out-of-form Buccaneers this time round as coach Kjell Jonevret targets silverware.
KwaDukuza defeated Ajax Cape Town on penalties in their Last 32 clash and will hope for a similar result when they host SuperSport.
Other Last 16 games see Chippa United host Polokwane City, Bloemfontein Celtic entertain National First Division side Mbombela United, BidVest Wits travel to second-tier side Jomo Cosmos and Baroka FC host Platinum Stars.
The matches will be played between April 5-9, with the exact dates, times and venues to be announced by the Premier Soccer League in due course.
NEDBANK CUP LAST 16
Chippa United vs Polokwane City
KwaDukuza United vs SuperSport United
Bloemfontein Celtic vs Mbombela United
Free State Stars vs Orlando Pirates
Jomo Cosmos vs BidVest Wits
Baroka FC vs Platinum Stars
Mamelodi Sundowns vs Lamontville Golden Arrows
Acornbush United vs Kaizer Chiefs