Techniques for placement in highly constraint chip architectures are described herein. In an example embodiment, a computer system places a digital portion of an electronic design for a programmable chip. The programmable chip comprises multiple fixed-function blocks and a plurality of pins, where each one of the multiple fixed-function blocks can be coupled only to a respective subset of the plurality of pins. The electronic design comprises a particular fixed-function block (FFB) instance that is connected to a particular input-output (IO) instance. The computer system places (e.g., by using a backtracking search) the particular FFB instance on a particular fixed-function block and the particular IO instance on a particular pin from a particular subset of the plurality of pins, where in the programmable chip the particular fixed-function block can be coupled only to the particular subset of the plurality of pins.