Not if it's dark and he's running away with your jewelry or other property. Deadly force is authorized to stop or prevent "theft during the night" among other property crimes. Although fighting the resulting civil lawsuit will cost more than the deductable on your insurance, so it's probably not worth it, other than as fufilling a civic duty, after all the next time the criminal might hurt someone, if he is allowed to succeed.
From the Texas Penal Code (similar rules apply to protecting a third party's property):
§ 9.41. Protection of One's Own Property
(a) A person in lawful possession of land or tangible, movable property is justified in using force against another when and to the degree the actor reasonably believes the force is immediately necessary to prevent or terminate the other's trespass on the land or unlawful interference with the property.
(b) A person unlawfully dispossessed of land or tangible, movable property by another is justified in using force against the other when and to the degree the actor reasonably believes the force is immediately necessary to reenter the land or recover the property if the actor uses the force immediately or in fresh pursuit after the dispossession and:
(1) the actor reasonably believes the other had no claim of right when he dispossessed the actor; or
(2) the other accomplished the dispossession by using force, threat, or fraud against the actor.
Acts 1973, 63rd Leg., p. 883, ch. 399, § 1, eff. Jan. 1, 1974. Amended by Acts 1993, 73rd Leg., ch. 900, § 1.01, eff. Sept. 1, 1994.
§ 9.42. Deadly Force to Protect Property
A person is justified in using deadly force against another to protect land or tangible, movable property:
(1) if he would be justified in using force against the other under Section 9.41; and
(2) when and to the degree he reasonably believes the deadly force is immediately necessary:
(A) to prevent the other's imminent commission of arson, burglary, robbery, aggravated robbery, theft during the nighttime, or criminal mischief during the nighttime; or
(B) to prevent the other who is fleeing immediately after committing burglary, robbery, aggravated robbery, or theft during the nighttime from escaping with the property; and
(3) he reasonably believes that:
(A) the land or property cannot be protected or recovered by any other means; or
(B) the use of force other than deadly force to protect or recover the land or property would expose the actor or another to a substantial risk of death or serious bodily injury.
This is not true. If he has one of your possessions then you can chase him down to retrieve it. If there is then a threat, by him, to your life then you can shoot to stop him.
The only proviso is that if you lose sight of him you can continue to chase, but you cannot shoot to stop. You must back away and not press the issue further. If you do then you are up a creek.
On your property at night you can also shoot to stop just like if he was inside.
Eaker
If he is simply larger and/or younger and stronger than you, and attacking you with his fists, would that qualify? What amount of force being used against you would be required to justify shooting the guy there?