Will the original ceiling box in my 1939 home support a new 45lb chandelier?
If the support is as you illustrated, the weight is being held by screws through the support and vertically into the ceiling joist. The load is being held up by screws pointed upward. The strain is downward. All that is holding up the weight is the wood around the threads of two (or maybe four) screws.

In general, wood screws do best when the load is shear (perpendicular to the direction of the screw). Pullout loads are especially vulnerable in older wood that may be deteriorating over time and getting powdery. 1939 is not so old comparatively, but this situation is not ideal. 

You might want to consider a replacement box and support that wedges between two joists such as this one. On 16" centers, they are rated for up to 150 lbs and 50 lbs. on 24" centers. For fans, they are rated for less (70lbs. on 16") because of dynamic stresses.



These can be inserted in a 4" hole.

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