IIRC, Embraer nows owns the tooling and licences for the PA31 line and have / still do turn out Chieftains et al in Brazil..... They call them by the Piper model numbers, 1020 and 1040 I think.
Piper outsorced construction of PA31 to Brazil (NEIVA) Columbia and Argentina, the Brazillian ones were renumbered as EMB 820. There was a conversion called the Caraja which was PT6 powered. South American produced Pipers can not be registered in the USA, therefor they are valued a lot less. This clause is listed on the TCDS and is governed by the aircrafts serial number.
The T-1000 series was developed by Piper for use by commuter airlines, these were produced in the USA. The T-1020 is a Chieftain with reduced weight and a basic 11 seat layout. The T-1040 is a Hybrid Chieftain/Cheyenne with turbine engines.