Yes! Precious is a legitimate name. Its usage goes all the way back to early Medieval England, and it was quite a common female name in its myriad forms across Western Europe.
It is first attested as a female given name in England in the year 1203, then again in 1279 and in 1327. It was common in Medieval Europe to give females names with nice attributes.
Preziosa appears in Medieval Italy and Preciosa is occassionally used among Spanish-speakers, sometime in reference to the Precious Blood of Christ.
Precious seems to have fallen out of usage by the 15th-century and was not revived until the late 20th-century. In the United States, it is more prevalent in the African-American community.
It is currently 958th most popular female name in the United States (2010).
Meaning: “precious glory.”
The name is composed of the Old Slavonic element, dorgu, meaning, “precious” and slav, meaning, “glory.”
The feminine form is Dragoslava (Southern Slavic, i.e. Bulgarian, Croatian, Macedonian, Serbian and Slovene) and Drahoslava (Czech/Slovak).
A Czech/Slovak masculine form is Drahoslav.
Name-days are January 4 (Slovakia) and January 17 (Czech Republic).
The designated name-days for the feminine version are: July 9 (Czech Republic) and September 1 (Slovakia)