* Correct Flywheel and Bellhousing: You'll need the correct bellhousing that's designed to mate the 700R4 to a small-block Chevy (SBC) engine. The 427 is a big-block Chevy (BBC), and the bellhousing is different. Therefore, you need an adapter plate or bellhousing specifically designed to mate a SBC transmission (like the 700R4) to a BBC engine. This is a crucial step; using the wrong parts will not work.
* Flexplate: You'll need the correct flexplate for a 700R4 transmission behind a big-block Chevy.
* Torque Converter: You'll need a torque converter designed for a 700R4 behind a big-block.
In short, while the transmission itself *isn't* directly compatible, with the right adapter/bellhousing and the correct flexplate and torque converter, you can successfully install a 700R4 behind a Chevy 427. This is a common modification, but it requires careful selection of the correct parts. Improper installation can lead to serious damage.