This op-amp buffer is oscillating and I can't figure out why

Chip suppliers are keen that their users avoid common design errors, shown by application examples in their data sheets. This one is addressed by Linear Technology in their data sheet for LTC6241. It also applies to many other opamps:

The good noise performance of these op amps can be attributed to large input devices in the differential pair. Above several hundred kilohertz, the input capacitance rises and can cause amplifier stability problems if left unchecked. When the feedback around the op amp is resistive (RF), a pole will be created with RF, the source resistance, source capacitance (RS, CS), and the amplifier input capacitance. In low gain configurations and with RF and RS in even the kilohm range (Figure 4), this pole can create excess phase shift and possibly oscillation. A small capacitor CF in parallel with RF eliminates this problem.

^{simulate this circuit – Schematic created using CircuitLab}