Unfortunately there is no shared deadline with these sorts of employment offers, so gamesmanship, departmental deadlines, and immediate teaching need combine together to make timing of interviews and offers almost universally inconvenient and stressful. Different tiers of university also know very well what sort of tier they are on, and they regularly strategically time their offer so it becomes a "one in the hand is worth two in the bush" style conundrum for candidates. I don't think I've talked with anyone who's gone through the process and never had a schedule issue of this sort.
So, let's unpack this a little and consider the options.
The chair is asking you if you'd be willing to take the offer without visiting the other schools is a feeler for how you view this particular position. Is this job a top choice for you, or just a backup plan that you'll take if nothing else comes through? And if something else does come through, will you drop them in a flash?
There's a good chance that they are seriously considering who would actually take the offer now and give up searching, so they know they'll actually get them on-board. No one wants to fail a search, because their work loads will increase or stay high because no one new has come on board, and they'll have to do this whole terrible process over again next year. It wouldn't be unusual for a department to have already failed a search last year, and this can happen multiple years in a row, so they may be really trying hard to avoid it again - but it's hard to say if this is the case here.
So, how do you answer? You should probably reiterate your interest in the position and the school, and that you'd be open to discussing the matter. This is non-committal, and probably is as diplomatic as I can imagine you can be.
The alternative of saying, "I'd be very interested in discussing an offer with you, but I couldn't possibly accept without completing some other interviews" could result in them giving you an offer anyway, and they may or may not be willing to give you more than 1-2 weeks to decide...but they might also just not give you an offer. They could even still give you an offer, but only if the other person(s) they give exploding offers to end up dropping out on them, and you become a last resort.
If you come right out and say "yes, I would absolutely be willing to respond to the offer without waiting", you'll kind of need to do that, because the offer will likely be only good for a week or so. I suppose you could backpedal and come up with an excuse as to why you can't respond in this deadline and ask for an extension, but if they've been so upfront about being unwilling to wait they might simply refuse.
They can say, "You can roll the dice and hope you get other offers, and we understand, but we are offering this position for certain right now, and our needs prohibit us from waiting longer as we must fill this position." Then you'll just have to weigh the risk vs the reward.
As with all negotiations, it's usually a game of power dynamics. Are you willing to walk away from the deal empty-handed? If so, then the ball is in your court and you can just be upfront, phantom offer notwithstanding, and they either give you an offer with a long deadline or they don't. If you aren't in that position of comfort (you don't have a backup plan you are willing to fall back to), then that greatly limits your ability to negotiate successfully and you just have to do what you can.