faSplit from Jim Kent's tools. Link for linux version.
chmod a+x faSplit after download.
faSplit - Split an fa file into several files. usage: faSplit how input.fa count outRoot where how is either 'about' 'byname' 'base' 'gap' 'sequence' or 'size'. Files split by sequence will be broken at the nearest fa record boundary. Files split by base will be broken at any base. Files broken by size will be broken every count bases.
For what you want
faSplit size input.fa 1000 outRoot
This breaks up input.fa into 1000 base chunks