This is for Ubuntu Linux 9.04.
Specifically, it is a 2-port eSATA PC-card with that VIA VT6421 chip. Inserting the card immediately results in the following added line in lspci output:
03:00.0 RAID bus controller: VIA Technologies, Inc. VT6421 IDE RAID Controller (rev 50)
hardware4linux.info says: this controller is supported, namely by kernel module sata_via [source].
Speaking of Ubuntu 8.04, it is reported that it does not automatically recognize new hot-plugged devices. To achieve that one has to execute
sudo scsiadd -s <channel no> (with the correct SCSI channel number) or
sudo scsiadd -s X. [source]
modprobe sata_via results in
FATAL: Module sata_via not found., but this might just indicate that this driver is built directly into the kernel (is not a module), to enable booting from SATA disks or something.