Paris Hilton is movin' on and movin' up ... to Malibu! The heiress was stunning as she went house hunting for a summer rental in Malibu -- she wore a long, flowing baby blue lace dress with heels and carried her cutest accessory -- her adorable little Chihuahua!

Ms. Hilton is gearing up for a HOT summer in the 'Bu, where she always rents a super-amazing home and hosts BBQs and beach parties and this summer will be no different!

The question is -- who's the dude?! Paris broke off her engagement to Chris Zylka late last year and has she replaced him with this cutie? We're not sure if they're just friends or what ... but we'll get the story and bring it to you!