Could it be as simple as the pull chain slipping off the pulley and wedging itself between the pulley and another part of the mechanism that's close?
It's really hard to tell unless someone goes up on a ladder and takes a close look. The mechanism itself is very simple but it has parts made of plastic that may be broken off or bent and the issue should be apparent when you just look at it up close. The metal rod that the pulley is turning, could be rusting if this is a bathroom, and that should also be visible from up close. Â If no apparent issue jumps out on you when you're up there, you'll have to take the vanes off, then bring the headrail down and inspect it. The vanes (louvers) usually just clip onto the sliders and can be easily undone with a stiff card (an expired credit card or a hotel card key works wonders). The headrail also normally just clips on two brackets on either side of the window. A slotted screwdriver may be needed to hold the spring clip when you take them off.
When the headrail is down, take the end cap at the chain end off and take a closer look. Once again, the mechanism is so simple, the reason for the jam should be clearly visible and fixable once you have access to the right part.