Try a couple of rubdowns with saddle soap.

I hate to get in the middle of a domestic quarrel, but that looks like a vintage leather club chair -- the sort of chair many people long for and pay hundreds of dollars for. (Your "stain" is what they call "patina.")

This type of chair looks its best in a clubby English/Ralph Lauren or World of Interiors-type decor.

Take him to one of those places with a huge brown club chair selection and let him know he can move on to new furnishings without breaking with the past. Other than that, throw it out when he's not looking and tell him it was stolen.

to me it looks less like a patina and an actual stain. Around the top you can see the sharp edge where the stain stops, a patina is usually a little more smooth and gradual. Like on the arms it looks like it has worn with age nicely, but the back looks horrible.

I would suggest Saddle Soap, read the directions and take your time. If it is an oil stain sometimes baby power can be used to soak up some of the oil.

Also would suggest Neats Foot Oil. Not sure of the spelling but you can find it in a shoe store.
Careful because it is a conditioner so Neatsfoot will change the entire complexion of the chair. Maybe just do the back panel and stop at the seams.

I would either persuade him into finding a newer chair in better condition like it or well toss it.

I think if you had a few other old things in the room, the contrast of the chair would be less jarring. You're not doing it any favors by placing it next to a white atomic table and modern white lamp.

I'm assuming it's the comfort of the chair your husband is attached to? Try reupholstering or put a custom slipcover on it in a "manly" fabric like denim, or, if you've got the $$ in leather.

If it's the leather he's crazy about and you can't reupholster, try visiting an established shoe repair place with the cushion to ask about dyeing options; you're looking for a place with an older craftsman with a lot of experience. You might be able to dye it black or extremely dark brown.

That stain would freak me out because mattresses with huge stains like that are generally that way because someone died in the bed. I know that sounds macabre and disgusting, but that's what it looks like to me. That chair gives me the creeps.

What about a throw blanket placed over the back?

Like the other's have said - That's called Patina.

People spend thousands to go to France and buy vintage club chairs with a patina like this and ship them home...

Your husband has a great eye for furniture - give him a little credit and leave his chair alone.

A friend of mine restores old BMW cars and he successfully dyes old leather seats. It can be done and it looks great!

You know, my husband also has a piece of leather furniture that he is really attached to. An old beat-up leather club chair - the cushion finally went on it and I took it to a shoe repair place to be fixed. While there, they dyed the leather (without asking!) - when I saw it, I was really surprised. The patina was still there but the colour was more uniform. A big improvement! So much so that I moved it into our living room, we get lots of compliments on it. My advice - consider asking someone that works with leather what they think. Take it a cushion to a shoe repair store, you might be surprised at what they tell you.

That's years of human oil secretions and general ick. This chair needs to be cleaned and conditioned by a leather care expert, assuming that it is well made enough to spend the money.

That is not patina - it is clearly a stain - I really wouldn't be happy sitting in this chair but if you can't persuade him to swap it for a new one in the same style (and you can get ones that look nice and "aged" already without harbouring the stains from a person!!) then take it to a professional to be cleaned