Do you have other pets? Dog? Cat? I'm not advocating tossing the chick in with a dog or cat but it sometimes happens that an animal of another species will adopt a baby chick. It's possible, not probable.
Baby chicks can imprint on another species and will form a bond. It's not the same as having a flock, but it can substitute for it. Single chickens can bond with a goat, a dog, a human.
Or you can search for a wind up fluffy toy that the chick can find comfort from. Even a mirror, as someone already suggested, can fool a chick into thinking another chick is present. I've had somewhat success with a mirror keeping a baby chick content, especially putting the chick food in front of the mirror to encourage the chick to eat.
If you have a heating pad, try fashioning it into a tunnel and scrunch up some soft fabric like velour or polartech so the chick can snuggle against the softness and warmth. If you provide it with darkness and warmth at night, it might be more content than kept under a heat lamp 24/7, and you might be able to get some rest, yourself.