Yes, but that'll destroy both and create other havoc.
Placing a bag of holding into an extradimensional space created by a Heward's handy haversack, portable hole, or similar item instantly destroys both items and opens a gate to the Astral plane.... (DMG p.154)
So the question, then, is whether a bag of holding, itself, creates such a space and is thus a similar item.
(And it's tempting to think that it's not: the bag's own description doesn't say that the interior is extradimensional, just that it's larger than the outside. For comparison, both the haversack and the hole do explicitly say early in their descriptions that they create extradimensional spaces.)
But the bag does create an extradimensional space. We know this from the descriptions of the handy haversack and portable hole, each of which list the bag of holding as creating one of these dangerously-incompatible spaces.
See DMG pp. 153-4, 174, and 186-7 for all descriptions.
Later, Mearls agrees. Remember, his rulings are not authoritative, but rather are just the word of one very well-informed GM.