How much can you compress a bitcoin for storage? I've just implanted an NFC chip in my hand and I'm wondering if a bitcoin will fit in the chip. it has a capacity of 868 bytes.
"A bitcoin" is not really a single concept. A bitcoin can be composed of 1000 outputs worth 0.001 BTC each, or 1 output worth 1 BTC, or any other such combination.

Bitcoin outputs are linked to private keys (for standard outputs). There are many ways to derive and encode private keys, and each of them would certainly fit in 868 bytes. However, you would likely have to extract the key into another device to actually use to to access your coins, which could be a security issue. You will most likely be better served, and more secure, by buying a hardware wallet.