I had been planning on it but as it isn't supported in the version of avr-gcc used in the standard Arduino IDE, I haven't yet bought one of the chips.
As a start though, I have found that somebody has got AVRDUDE to program them. [Code below sourced from here: http://www.avrfreaks.net/index.php?name=PNphpBB2&file=viewtopic&p=1121049 ]
Add this to the avrdude.conf
#------------------------------------------------------------
# ATtiny841
#------------------------------------------------------------
part
id = "t841";
desc = "ATtiny841";
has_debugwire = yes;
flash_instr = 0xB4, 0x07, 0x17;
eeprom_instr = 0xBB, 0xFF, 0xBB, 0xEE, 0xBB, 0xCC, 0xB2, 0x0D,
0xBC, 0x07, 0xB4, 0x07, 0xBA, 0x0D, 0xBB, 0xBC,
0x99, 0xE1, 0xBB, 0xAC;
## no STK500 devcode in XML file, use the ATtiny45 one
stk500_devcode = 0x14;
## avr910_devcode = ?;
## Try the AT90S2313 devcode:
avr910_devcode = 0x20;
signature = 0x1e 0x93 0x15;
reset = io;
chip_erase_delay = 4500;
pgm_enable = "1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1",
"x x x x x x x x x x x x x x x x";
chip_erase = "1 0 1 0 1 1 0 0 1 0 0 x x x x x",
"x x x x x x x x x x x x x x x x";
timeout = 200;
stabdelay = 100;
cmdexedelay = 25;
synchloops = 32;
bytedelay = 0;
pollindex = 3;
pollvalue = 0x53;
predelay = 1;
postdelay = 1;
pollmethod = 1;
hvsp_controlstack =
0x4C, 0x0C, 0x1C, 0x2C, 0x3C, 0x64, 0x74, 0x66,
0x68, 0x78, 0x68, 0x68, 0x7A, 0x6A, 0x68, 0x78,
0x78, 0x7D, 0x6D, 0x0C, 0x80, 0x40, 0x20, 0x10,
0x11, 0x08, 0x04, 0x02, 0x03, 0x08, 0x04, 0x0F;
hventerstabdelay = 100;
hvspcmdexedelay = 0;
synchcycles = 6;
latchcycles = 1;
togglevtg = 1;
poweroffdelay = 25;
resetdelayms = 0;
resetdelayus = 70;
hvleavestabdelay = 100;
resetdelay = 25;
chiperasepolltimeout = 40;
chiperasetime = 0;
programfusepolltimeout = 25;
programlockpolltimeout = 25;
ocdrev = 1;
memory "eeprom"
size = 512;
paged = no;
page_size = 4;
min_write_delay = 4000;
max_write_delay = 4500;
readback_p1 = 0xff;
readback_p2 = 0xff;
read = "1 0 1 0 0 0 0 0 0 0 0 x x x x a8",
"a7 a6 a5 a4 a3 a2 a1 a0 o o o o o o o o";
write = "1 1 0 0 0 0 0 0 0 0 0 x x x x a8",
"a7 a6 a5 a4 a3 a2 a1 a0 i i i i i i i i";
loadpage_lo = " 1 1 0 0 0 0 0 1",
" 0 0 0 0 0 0 0 0",
" 0 0 0 0 0 0 a1 a0",
" i i i i i i i i";
writepage = " 1 1 0 0 0 0 1 0",
" 0 0 x x x x x x",
" x a6 a5 a4 a3 a2 0 0",
" x x x x x x x x";
mode = 0x41;
delay = 6;
blocksize = 4;
readsize = 256;
;
memory "flash"
paged = yes;
size = 8192;
page_size = 16;
num_pages = 512;
min_write_delay = 4500;
max_write_delay = 4500;
readback_p1 = 0xff;
readback_p2 = 0xff;
read_lo = " 0 0 1 0 0 0 0 0",
" 0 0 0 0 a11 a10 a9 a8",
" a7 a6 a5 a4 a3 a2 a1 a0",
" o o o o o o o o";
read_hi = " 0 0 1 0 1 0 0 0",
" 0 0 0 0 a11 a10 a9 a8",
" a7 a6 a5 a4 a3 a2 a1 a0",
" o o o o o o o o";
loadpage_lo = " 0 1 0 0 0 0 0 0",
" 0 0 0 x x x x x",
" x x x a4 a3 a2 a1 a0",
" i i i i i i i i";
loadpage_hi = " 0 1 0 0 1 0 0 0",
" 0 0 0 x x x x x",
" x x x a4 a3 a2 a1 a0",
" i i i i i i i i";
writepage = " 0 1 0 0 1 1 0 0",
" 0 0 0 0 a11 a10 a9 a8",
" a7 a6 a5 x x x x x",
" x x x x x x x x";
mode = 0x41;
delay = 6;
blocksize = 32;
readsize = 256;
;
# ATtiny841 has Signature Bytes: 0x1E 0x93 0x15.
memory "signature"
size = 3;
read = "0 0 1 1 0 0 0 0 0 0 0 x x x x x",
"x x x x x x a1 a0 o o o o o o o o";
;
memory "lock"
size = 1;
write = "1 0 1 0 1 1 0 0 1 1 1 x x x x x",
"x x x x x x x x x x x x x x i i";
read = "0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0",
"0 0 0 0 0 0 0 0 o o o o o o o o";
min_write_delay = 9000;
max_write_delay = 9000;
;
memory "lfuse"
size = 1;
write = "1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0",
"x x x x x x x x i i i i i i i i";
read = "0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0",
"x x x x x x x x o o o o o o o o";
min_write_delay = 9000;
max_write_delay = 9000;
;
memory "hfuse"
size = 1;
write = "1 0 1 0 1 1 0 0 1 0 1 0 1 0 0 0",
"x x x x x x x x i i i i i i i i";
read = "0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0",
"x x x x x x x x o o o o o o o o";
min_write_delay = 9000;
max_write_delay = 9000;
;
memory "efuse"
size = 1;
write = "1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0",
"x x x x x x x x x x x x x x x i";
read = "0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0",
"x x x x x x x x o o o o o o o o";
min_write_delay = 9000;
max_write_delay = 9000;
;
memory "calibration"
size = 1;
read = "0 0 1 1 1 0 0 0 0 0 0 x x x x x",
"0 0 0 0 0 0 0 a0 o o o o o o o o";
;
;