My assumption is that it is related to the output capacitor, specifically, the ESR of the output capacitor - similar to a problem I had with a linear voltage regulator. I thought I'd ask before starting a cycle of de-soldering/re-soldering.
Channel 2 is the 5V input to the IC and is stable. Channel 1 is the oscillating output.
The TI datasheet requires an output capacitor of 1uF to 50uF with an ESR of 1.0 to 1.5 ohms. I don't have prior experience of this IC to know what would work but it would seem 'others' have used 10uF or 22uF caps. As usual, the capacitor datasheet isn't much use for determining ESR at DC frequency but it could be that C45 has too high an ESR (it's specced at 0.7Ohms at 100kHz but goes higher at lower frequencies.) The components attached to the Trim/NR pin are from the datasheet for reducing noise (at the expense of startup time) and allowing a trim of +-15mV.