Thank you for your reply RoGeorge!
I am using a cheap Chinese (P6100) 100MHz passive probe at 10X and calibrated to the scope. Attached is a collage of screenshots:
The issue is neither with your scope nor your probe.
The square wave from the calibration signal of the scope proves that the scope is perfectly capable of displaying a square wave. The timebase used for that is 400 us, and the wave requires 2.5 divisions, which translates to 1 ms, to complete a cycle, making it a 1 kHz square wave.
The sine wave from the crystal is being shown with a 2 ms timebase, and a cycle takes 0.5 divisions, which translates to 1 ms, to complete a cycle, so it, too, is a 1 kHz signal.
No, what's being generated by the crystal is clearly a sine wave.
Note that for anything more than about 1 MHz, you should be using a 1:10 probe. Most cheap probes have a switch that lets you select "1x" or "10x", the latter of which being what you want to use for anything of any reasonable frequency, and is also what you need to have selected when you're performing compensation adjustments to your probe. You need to tell the scope that you're using a 1:10 (i.e. "10x") probe under those conditions so that it will display voltages properly.