Technically and simply, no.
“Chief” is what the title means. It applies to all such roles: one Chief of Technology, the Chief of Marketing… you’re proposing two people equally but completely in charge of the executives.
So, in whom do I take direction when you both disagree?
Wanting to be CEO tells me you both have an ego problem, frankly. Who cares what your title is unless you do. The title means something; you are it or you’re not, and two wanting to be it means neither of you are acting as through you are it.
Keep in mind, CEO doesn’t mean boss. This isn’t a sole proprietorship and a CEO isn’t the manager or person in charge. They’re a role; the chief role, granted, but a distinct role.
Generally, the CEO is responsible for resources and attention, as well as keeping the exectives on track with the vision. That it, enabling THEM to lead and manage.
Which of you two is doing that?
There are other, loosely related roles, nearly akin to CEO, that have other distinct titles.
One of you might be better as COO… they essentially run the operations of the company: HR, finances, legal, and project management. They’re in many ways more of a boss than the CEO.
Maybe one of you is the President. Typically, more involved in day to day business decisions so the CEO can go do their job.
Our company is run like this. Frankly, I rather suck as holding people accountable and I’m not a hardass on people who aren’t pulling their weight. It’s just not in nature. But, I’ve inspired, have a vision, and drive demand and excitement for what we’re doing. I’m a CEO who needs and President and COO to run our company. Buck stops with me, but my decisions are more like as Captain of a starship, I don’t run engineering and Number One really runs the ship, I make some of the hard decisions and keep us boldly going where no one has gone before.