Electronic – PIC 16F84A RC oscillator problems

I'm trying to use an RC oscillator on a PIC 16F84A-20 that I have on a breadboard. The code is supposed to (at this point) simply flip an output back and forth every so often.

I don't need it to run very fast, so I figured I'd try using the RC network on CLKIN instead of a crystal. My problem is that my code doesn't seem to be running consistently (I get some LED flashes for a few seconds, then nothing, then perhaps more flashes, etc).

I'm working on a plug-in breadboard. I've got +5 provided by a PIC dev board I had handy.
+5 is reading 4.94 volts via my DMM.
I used a 4.7K resistor from CLKIN to +5, and a 33pf cap to GND.

I put an o-scope on CLKIN, and I see a sawtooth-ish wave of about 2.5Mhz, but I also see some other, longer waveform in the background, if you will (it's far fainter than the sawtooth). it's a much wider, slowly decaying pulse. The sawtooth wave is, unfortunately, only about .2-.3 volt high, and centered between +5 and GND.

I put the scope on CLKOUT, and in the instances where I'm seeing my LEDs blink, I've got a nice squarewave on CLKOUT. Other times it's just flat.

My assumption is that I've made some basic error with the RC circuit that's causing it to not generate a sufficient waveform, and thus not work. I'd like pointers to what I should be checking next.