[polexia]

A carbene is a "neutral carbon atom with two substituents and a lone pair of electrons.

Cl---  C·· ---Cl  Carbon has two electrons less than an octet, so wouldn't it be positive?

I'm thinking in the line of... a carbocation intermediate

R---C----R  This carbon also has two electrons less than an octet and it is considered positive.
      R

[discodermolide]

A carbene is a neutral species.
http://en.wikipedia.org/wiki/Carbene

[opsomath]

This is a very interesting question, because it points up a basic logical fallacy.

"Carbocations are positive. Carbocations have two electrons less than an octet. Carbenes have two electrons less than an octet. Therefore, carbenes are positive." is a fallacy. The properties "full octet" and "positive" are independent of each other. For instance, ammonium (NH4+) is positive, but the center N has a full octet. OTOH, borane (BH3) is neutral, but the central boron lacks an octet. (In fact, borane is "isoelectronic" to a methyl carbocation, meaning that it has the same number of electrons; the only difference is that the carbon center has one more proton in its nucleus, so the whole thing is positive.)

You may want to review how to calculate formal charges. Basically, you can think of a carbene as a carbocation except that one of its bonds has been replaced with a lone pair, so it gets an extra electron formally located around that center.