Yes, this is possible, as long as you use a bootloader that understands RAID-1 and LVM. Grub 2 (i.e. Grub 1.9x — LVM and RAID support started in Grub 1.95) does, LILO (non-antique) does, Grub 1 (i.e. Grub 0.9x) does not.
Source: I've done it. Also:
GRUB 2 can read files directly from LVM and RAID devices.
Grub 1 or any other bootloader has no trouble with RAID-1, it just reads from one of the volumes (you can even retain the ability to boot without intervention if one of the mirror halves fails with the right BIOS and boot sector setup). But Grub 1 doesn't understand LVM, so you need a non-LVM
Note that Grub 2's RAID modes might lag behind Linux's, so in a given distribution, there may be RAID arrangements that the Linux kernel and userland tools support perfectly but Grub chokes on. For example, in Ubuntu 10.04, Grub2 did not support mdraid RAID-1 with the 1.0 metadata format (with metadata at the start of the volume). By Ubuntu 11.10, Grub2 supported this mode. I don't know the exact version threshold (1.97?).