Are you running a toyota oil filter? Most aftermarket filters don't have the anti-drainback valve that keeps oil pressure on the timing chain tensioner. You might try switching to the good Toyota Japanese filter ( The last 2 digits of the part number are D1 - if you get a filter with the last 2 digits 11, it's not what you want) and see what happens. Expect to pay around $6 at your local dealership...
That may be all you hear- I've seen a few of these at work lately, as the temp has dropped around here.
Good luck,
Ryan