Lewis Structure of BCl3, Boron Trichloride (and Hybridization)

​Boron Trichloride, BCl3, has three chlorine atoms surrounding a single boron atom.

This is because each chlorine brings seven valence electrons with it, and needs just one more electron to complete its octet.

Boron has three valence electrons to start with, but does not need a full eight electrons to be stable. It is a violation of the octet rule, but this is the way things are.
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So, Boron shares ONE electron with each of three chlorine atoms, and each chlorine shares one electron with Boron:

The Lewis Structure of Boron Trichloride (BCl3) has three chlorine atoms surrounding a single boron atom.

​This is a trigonal planar arrangement and implies that the boron must be sp2 hybridized. The extra unhybridized p orbital is empty, but its presence is what keeps the three sp2 orbitals separated by exactly 120 degrees.
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I have a video where I draw this Lewis Structure, if you're a visual learner:

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​Now, in reality, solid BCl3 is more complicated. The lone pairs on each chlorine atom are attracted to the wide-open slightly-positive charge on the Boron atom, and a Lewis Acid-Base reaction happens: That's fancy chemistry talk for chlorine sharing its lone pair with boron.

This gives the boron atoms in solid BCl3 a tetrahedral geometry; since each of them actually connect with FOUR chlorines each. It makes the entire structure more like a lattice, rather than being individual molecules.