It may help if you say why you need to do this & on which sites the large files are situated.
Never heard of such an online service, but the best I can offer is to use a download manager (see below) to download the file, then a free file splitter to split it up (if you still need to do so).
Orbit Downloader click here, has a pause function if you need to keep stopping & starting the large download (or even shut down your PC & continue downloading the next day, etc). G
P.S. If the large files are available on a P2P network, you could use a P2P program. But be aware of the potential dangers, pitfalls & possible copyright issues that such a service carries with it.