Kate Middleton A Shot in the Arm, Pleeeze!!!

Kate Middleton and Meghan Markle may have something in common ... they've both gotten vaccinated.

You'd think Kate would be fully vaccinated by now, but nope ... she got her first shot Friday at the London Science Museum. Seems London's a little behind the U.S. of A. in the vaccine department ... Kate, who's under 40, just became eligible.

Kate said after getting poked, "Yesterday, I received my first dose of the COVID-19 vaccine ... I'm hugely grateful to everyone who is playing a part in the rollout. Thank you for everything you are doing," adding she's "hugely grateful."

Her hubby, Prince William, got his shot a few days before at the same site.

It's unclear which vaccine they both received. They'd be entitled to either Pfizer or AstraZeneca.

Harry and Meghan have not confirmed that they are also fully vaccinated, but have encouraged the vaccine effort at events such as "Vax LIVE: The Concert to Reunite the World."

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