Can the Product Owner speak at the Daily Scrum?

In a nutshell, "Yes."

In the Scrum framework, the Daily Scrum is a collaborative planning event to adapt the team's plan based on current progress towards the Sprint Goal. The 2020 version of The Scrum Guide states that this event is "for the Developers." Earlier versions of the Scrum Guide went so far as to state that "The Scrum Master enforces the rule that only Development Team members participate."

This limitation to "Developers" is what has likely led to some confusion over whether the Product Owner is allowed to speak or participate at all in this event.

So why do I state unequivically, "Yes, the Product Owner can speak!"?

Well, let's look at The Scrum Guide for some clarification around this rule limiting participation to Developers.

In the first published version of The Scrum Guide in 2010, the wording around the Daily Scrum included "The ScrumMaster also enforces the rule that chickens are not allowed to talk or in anyway interfere with the Daily Scrum." This reference to "chickens" was inspired by a story about a chicken and a pig that was told in early teachings and writings about Scrum. While this story has fallen out of fashion in the Scrum community, I'll relate it here so that you have the context:

A chicken and a pig are together when the chicken says, "Let's start a restaurant!"
The pig thinks it over and says, "What would we call this restaurant?"
The chicken says, "Ham n' Eggs!"
The pig says, "No thanks, I'd be committed, but you'd only be involved!

So who were the chickens and who were the pigs in Scrum?

Well this is where it might get a bit more confusing. Stay with me now...

While we currently call the people who do the work of turning Product Backlog items into working increments "Developers", the 2010 version of The Scrum Guide called these same people the "Team" as in "The Scrum Team consists of the ScrumMaster, the Product Owner, and the Team." That Team within a Scrum Team taxonomy also led to some confusion and is one reason that Developers is the new name for this group of "workers".

Now back to the chicken and the pig...

The 2010 version of the Scrum Guide continues:

"Scrum Team members are called 'pigs.' The Product Owner is the 'pig' of the Product Backlog. The Team is the 'pig' of the Sprint work. The ScrumMaster is the 'pig' of the Scrum process. Everyone else is a 'chicken.' Chickens cannot tell 'pigs' how to do their work."

So this seems clear — ALL Scrum Team members were pigs, including the Product Owner. The instruction that the Scrum Master enforce the rule that chickens are not allowed to talk does not apply to the Product Owner since they were explicitly a pig!

Thankfully, the whole story of the chicken and the pig has faded into ancient Scrum history, and now the 2020 version of The Scrum Guide explains with clarity and simplicity about Daily Scrum participation:

"If the Product Owner or Scrum Master are actively working on items in the Sprint Backlog, they participate as Developers."

So yes, if your Product Owner is helping the team with the work in the current Sprint (it would be surprising if they are totally disengaged), they have earned a place in the Daily Scrum and the event is likely to be richer and more collaborative than it would have been otherwise.