A worker trims cannabis at the growing facility of the Tikun Olam company on March 7, 2011 near the northern city of Safed, Israel.

Shares of Canadian cannabis producer Tilray posted their second-best day ever after the company announced approval from the Drug Enforcement Administration to import marijuana to the United States for medical research.

The company's U.S.-listed shares jumped 28.9 percent Tuesday with 19 million of the company's 21.7 million floating shares exchanging hands. Shares are up over 400 percent in the past month.

Tilray will work with the University of California San Diego Center for Medicinal Cannabis Research to study the safety, tolerability and efficacy of marijuana for a neurological disorder.

"Tilray is proud to support this crucial research," says Dr. Catherine Jacobson, director of clinical research at Tilray.

"If this study can identify cannabinoids as a potential treatment for patients suffering from essential tremor, we can conduct further research and potentially provide alternative effective methods of relief for the high numbers of patients with Essential Tremor," she added.

Essential Tremor is a neurological movement disorder characterized by involuntary and rhythmic shaking, according to the company's website. Tilray added that ET affects 0.4 percent of the general population, with 4.6 percent to 6.3 percent of those 65 and older suffering from the condition.

The UC San Diego clinical trial marks the fifth worldwide using Tilray's cannabis. Other trials include a study at the University of British Columbia Okanagan on the impact of cannabis on post-traumatic stress disorder, a trial at the University of Sydney in Australia on chemotherapy nausea reduction and a study at The Hospital for Sick Children in Toronto on pediatric epilepsy.

Tilray CEO Brendan Kennedy says clinical trials are a very important part of the company's strategy.

"Clinical trials build a halo around the brand. They inspire confidence and trust with physicians and regulators around the world and they give us data and information to talk to pharmacists and physicians that they just can't obtain from our competitors," Kennedy said.

And in many cases, Tilray has a leg up on marijuana companies local to a particular study. In the U.S., for example, strict regulations governing marijuana, which is still illegal under federal law, force research facilities to acquire federally approved cannabis products from a very short list of suppliers. Plant material can come exclusively from the University of Mississippi, which is authorized by the National Institute on Drug Abuse. A few other companies offer plant-derived pharmaceuticals and synthetic cannabinoids for research. The limited number of providers means they may not have the specific formulation a study requires.

Beyond legal restrictions, Tilray has the advantage of experience, Kennedy said. The company is licensed by the federal government of Canada, has passed quality control inspections from dozens of partners — from pharmaceutical distributors and retailers to the governments of foreign partners — and its product is pharmaceutical grade.

If a licensed medicine were to come out of the clinical trials, Tilray would own the intellectual property rights, which could be hugely lucrative for the company. But Kennedy emphasized that even if that doesn't happen Tilray still hopes to participate in as many trials as possible.

"We would participate in these clinical trials even if we knew no licensed medicines were going to come out of them. It gives us data, it gives us information, it gives us dosing data, and that information enables us to educate and inform physicians and pharmacists around the world," Kennedy said.

Wall Street, meanwhile, heralded the go-ahead as a sign that the DEA is standing by its goal to improve resources and cannabis research. Tilray's market cap, despite the company posting $9.7 million in revenue as of last quarter, is larger than more than one-quarter of the S&P 500.

For reference, the company's valuation exceeds that of Chipotle and E-Trade.

"Today's news is a positive for both Tilray and the broader cannabis stock universe, as additional medical applications and improved government support add another domino to future legalization in the U.S.," wrote Cowen analyst Vivien Azer.

"Further, the new clinical trial supports Tilray's medical cannabis prospects (both in U.S. and globally) as it competes with Canopy Growth (39 U.S. patents and 15 clinical trials) in an intellectual property-arms race," the analyst added.

Programming Note: Tilray CEO Brendan Kennedy will appear on Mad Money tonight on 6 p.m. ET.

— CNBC's J.R. Reed contributed reporting.