Very rare occurrence in LA.
Indeed very rare but not unknown...
http://neic.usgs.gov/neis/states/louisiana/louisiana_history.html
This quake today appears to be in the same area as the estimated Magnitude 4.2 quake in 1930 described below...
...An earthquake centered about 60 miles west of New Orleans awakened many people throughout eastern Louisiana at about 6:17 a.m. on October 19, 1930. Maximum intensity reached VI at Napoleonville, where the entire congregation rushed from a church, as the entire building rocked noticeably. Intensity V effects were noticed at Allemands, Donaldsonville, Franklin, Morgan City, and White Castle, where small objects overturned, trees and bushes were shaken, and plaster cracked. The total felt area was estimated at 15,000 square miles, based on a detailed questionnaire canvass of the region surrounding the epicenter. The historical files of Prof. Harry Fielding Reid, Johns Hopkins University, were searched in order to find data on earlier shocks in the area. Slight tremors were listed on February 14, and 15, 1843, and April 1882. There also was a slight earthquake on the Mississippi Delta at Burrwood on December 15, 1927...
...On November 19, 1958, a local earthquake in the Baton Rouge area shook houses and rattled windows. Scores of residents telephoned the Weather Bureau, Civil Defense, police and radio stations. The shock was also felt at Baker and Denham....