I have run several experiments using this amp with headphones:
1. Connecting headphone jack to outputs, connecting -ve speaker leads together: DOES NOT WORK, could damage amplifier.
2. Isolating headphone transducers (separating -ve leads, connecting like speakers to amp output): if possible (not all phones permit this, and this can be challenging if headphone leads are litz wire or similar): works fine, excellent sound quality, strongly recommended.
3. (Most recent) Connecting 8 ohm wire wound resistors in series with negative outputs of amplifier to negative terminal of standard (3 wire) headphone jack: WORKS with Koss Pro4AAs (low impedance) headphones, sound quality excellent. Need to test with other models, though. Approach (2) will work with any applicable phone.
Please note: I have tested using 3 different Lepai 2020 amps, one an early version (claiming output of 550W printed on top of case, obviously either a misprint or old fashioned Communist propaganda) and two more recent (with tone defeat switches(. All 3 are noiseless into tested headphones. I see comments regarding hum/noise problems with individual Lepai 2020 samples--I would recommend changing power supplies first, and if problem persists, get a replacement from PE, since these amps clearly should be noiseless if operating properly. However, before changing anything, plug your signal source into a known good amplifier, since T-amps have a habit of displaying signal source problems in high relief due to their superior fidelity to the source.
If operating (and operated) properly, these little amps rate among the best I have heard (and in 50+ years of critical audiophile listening, I have heard plenty). Also, for those of you who think that 60+ yo ears must be impaired, I can still sense >10KHz signals with mine. (Must be all those thermonuclear powered rock concerts I never attended when I was younger)